12. Find one solution for each equation. Assume all angles are acute angles
a. cos(0 + 4°) = sin(30 +2°)
Answer:
21 degrees
Step-by-step explanation:
I'm assuming that the 0 is supposed to be theta, which I'm replacing with x to make it easier for me to type.
Because these angles are acute, we can use the fact that if two angles A and B are complementary, then sinA = cosB.
So we can get that x+4+3x+2=90
4x+6=90
4x=84
x=21
Find the slope of each line points (3,4) and (5,4)
Step-by-step explanation:
Slope formula:
[tex] \frac{y2}{x2} - \frac{y1}{x1} = m[/tex]
m = slope
Substitute the points into the formula format:
[tex] \frac{4}{5} - \frac{4}{3} = m[/tex]
Solve:
[tex] \frac{0}{2} = m[/tex]
The slope is 0.
The line doesn't increase or decrease.
Solve for x.
−4/5x+3/10<8/10
Answer:
x > -5/8
Step-by-step explanation:
Simplify by combining x and 4/5 and then moving 4 to the left side of x
-x * 4/5 + 3/10 < 8/10
-4x/5 + 3/10 < 8/10
Now we cancel the common factor of 8 and 10.
Factor 2 out of 8
-4x/5 + 3/10 < 2(4)/10
2 from 10
-4x/5 + 3/10 < 4/5
Now move all the terms not containing x to the right side
Lets subtract 3/10 from both sides
-4x/5 < 4/5 - 3/10
Now we multiply by 2/2 to write 4/5 with a common denomi.
-4x/5 < 4/5 * 2/2 - 3/10
Now write with a common denom of 10 and multiply by 1
-4x/5 < 4*2/5 * 2 - 3/10
5 by 2
-4x/5 < 4 * 2/10 - 3/10
Combine
-4x/5 < 4 * 2 - 3/10
Simplify the numerator by multiplying then subtracting
-4x/5 < 8 - 3/10
-4x/5 < 5/10
Cancel the common factor of 5 and 10...
-4x/5 < 5(1)/10
-4x/5 5* 1/5 * 2
-4x/5 < 1/2
Now we divide by -1
-4x/5)/-1 > 1/2)/-1
4x/5 > 1/2)-1
4x/5 > -1/2
Multiply both sides by 5 and cancel common factors. (5)
4x * 5 > -1/2 * 5
4x > -1/2 * 5
4x > -5/2
Now divide by 4 in each term
4x/4 > -5/2)/4
x > -5/2)/4
Multiply the numer by the reciprocal of the denom
x > -5/1 * 1/4
x > -5/4 * 2
x > -5/8
A bakery give me three options 12 cupcakes for $29 24 cupcakes for $56 50 cupcakes for $129 find each unit price to the nearest cent
a = 29 / 12
b = 56 / 24
c = 129 / 50
a = 2.42
b = 2.33
c = 2.58
b is cheapest, 24 for $56
Help to solve for x by completing the square
here u go, if u need it clearer I will re write just tell me
Answer:10.4 or -0.4
Step-by-step explanation:
The explanation is in the attached file below
in the sequence 5,11,19,29,41
find the 25th term
Answer:
25th term = 701
Step-by-step explanation:
see attached
have a great day :)
I need help with math please
Okay, so the function is to do x times 2, then subtract 4.
6 x 2 = 12, 12 - 4 = 8. The first one is 8.
2 x 2 = 4. 4 - 4 = 0.
-4 x 2 = -8. -8 - 4 = -12. The last is -12.
With this information we can tell that it is C, 8, 0, -12.
90 kids in the band 20% of the kids own their own instruments how many kids own their own instruments
Answer:
18
Step-by-step explanation:
20% = .20
90 x .20=18
Hence, 18 kids own their own instruments
[RevyBreeze]
y=x+2
y+1= – 4x
Is this ordered pair a solution of the system of equations? Help:(
Put value of y in Equation 1 in Equation 2.
[tex] \looparrowright \sf y + 1 = - 4x[/tex]
[tex] \\ \\ [/tex]
[tex] \looparrowright \sf (x + 2) + 1 = - 4x[/tex]
[tex] \\ \\ [/tex]
[tex] \looparrowright \sf x + 2 + 1 = - 4x[/tex]
[tex] \\ \\ [/tex]
[tex] \looparrowright \sf x +3= - 4x[/tex]
[tex] \\ \\ [/tex]
[tex] \looparrowright \sf x + 4x= - 3[/tex]
[tex] \\ \\ [/tex]
[tex]\looparrowright \sf 5x= - 3[/tex]
[tex] \\ \\ [/tex]
[tex]\looparrowright \sf x= \dfrac{ - 3}{5} [/tex]
[tex] \\ \\ [/tex]
Let's find value of y :
[tex] \\ \\ [/tex]
[tex]\looparrowright \sf y=x+2[/tex]
[tex] \\ \\ [/tex]
[tex]\looparrowright \sf y= \dfrac{ - 3}{5} +2[/tex]
[tex] \\ \\ [/tex]
[tex]\looparrowright \sf y= \dfrac{ - 3 + 10}{5} [/tex]
[tex] \\ \\ [/tex]
[tex]\looparrowright \sf y= \dfrac{7}{5} [/tex]
Solution:
[tex]\looparrowright \sf \bigg( \dfrac{ - 3}{5} , \dfrac{7}{5} \bigg)[/tex]
Shaunda said that buying 4 towels for $17 was a better buy than buying 2 towels for $9. She found her answer by doubling the terms in the ratio 9/2 and comparing the first terms in the ratio. Is she correct? Use unit prices to support your answer
Answer:
The cost for a towel at 4 for $17 is:
17/4 = 4.25 $/towel
The cost for a towel at 2 for $9 is:
9/2 = 4.5 $/towel
So Shaunda is correct, as the cost per towel for 4 at $17 is lower.
I don't know how to do this
Answer: 2x+3 and -1
Step-by-step explanation:
a)
[tex]A=\pi r^2 = 4\pi x^2 + 12\pi x + 9\pi\\r^2 = 4x^2 + 12x + 9\\r^2 = (2x+3)^2\\r = 2x+3[/tex]
b) Radius has to be greater than 0, so 2x + 3 > 0
2x > -3
x > -1.5
So least possible integer value is -1
Find the value of xif 3(x + 5 ) =-6
Answer:
-7
Step-by-step explanation:
A equation is given to us and we need to find out the value of x . The given equation is ,
[tex]\longrightarrow 3( x +5)=-6 [/tex]
Simplify the parenthesis ,
[tex]\longrightarrow 3x + 3(5)=-6[/tex]
Simplify,
[tex]\longrightarrow 3x +15 = -6[/tex]
Subtracting 15 to both sides ,
[tex]\longrightarrow 3x =-6-15[/tex]
Simplify,
[tex]\longrightarrow 3x = -21 [/tex]
Divide both sides by 3,
[tex]\longrightarrow x = -7 [/tex]
This is the required answer!
If ∠JAM and ∠JAK are supplementary angles, then what is the measure of ∠KAL?
A.
60°
B.
33°
C.
55°
D.
57°
Answer:
D) 57
Step-by-step explanation:
180 - 123
pls can u gus tell me the ans and explanation
Step-by-step explanation:
the volume of the tank is
80×50×45 = 180,000 cm³
3/4 of that volume is
180000 × 3/4 = 135,000 cm³
so, we want to know how long it takes to fill 135,000 cm³.
the water intake flow is 9 l / minute.
now we need to know that a cube of 10 cm side length contains exactly 1 liter of water.
such a cube has the volume
10×10×10 = 10³ = 1000 cm³
so, 1000 cm³ = 1 liter.
and we need to fill 135,000 cm³.
how many times fit 1000 cm³ into 135,000 cm³ ?
135000/1000 = 135 times.
and that means it would take 135 minutes to fill it, if the flow was 1 l / minute.
but it is faster (9 times faster) : 9 l / minute
so, how many minutes ?
135 / 9 = 15 minutes
it takes 15 minutes to fill 3/4 of the tank.
Answer:
15 minutes
Step-by-step explanation:
The volume (V) of the tank is calculated as
V = lbh (l is the length, b the breadth and h the height (
here l = 80, b = 50, h = 45 , then
V = 80 × 50 × 45 = 180000 cm³
1 litre = 1000 cm³ , then
9 litres = 9 × 1000 = 9000 cm³
Divide the volume of the tank by 9000 for time in minutes
180000 ÷ 9000 = 20 minutes
It takes [tex]\frac{3}{4}[/tex] × 20 = 15 minutes to fill [tex]\frac{3}{4}[/tex] of the tank
Lesson 13 Exit Ticket 5.4
Name
Date
1. Solve. Draw a rectangular fraction model, and write a number sentence to show your thinking.
I do not know how to do this
A rectangular fraction model can be drawn based on this idea: Annie had a total of cookies 20 but she gave 9 cookies to her friends, how many cookies does she have?
What is a rectangular fraction model?A rectangular fraction model refers to using a rectangle and dividing it to represent and understand fractions. This might be easier than representing fractions by only using numbers.
How to draw a rectangular fraction model?The first step is to think about a possible situation or word problem. After this, you can draw the fraction model. For example:
Annie had a total of 20 cookies but she gave 9 cookies to her friends, how many cookies does she have?For this, divide a rectangle in the total of parts (20) and color the total of parts that Annie has (11). This means the total of cookies she has is 11/20.
Learn more about rectangles in: https://brainly.com/question/10046743
The equation of line p is y=−4x+1. Line q is perpendicular to line p and passes through (−4, 1). What is the equation of line q?
Write the equation in slope-intercept form with no spaces. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.
Answer:
[tex]\displaystyle y = \frac{1}{4}\, x + 2[/tex].
Step-by-step explanation:
The question is asking for the slope-intercept equation of a line. The slope-intercept form equation of a line is in the form [tex]y = m\, x + b[/tex], where:
[tex]m[/tex] (a constant) is the slope of the line, and[tex]b[/tex] (also a constant) is the [tex]y[/tex]-intercept of that line.For example, the equation of the first line, [tex]y = -4\, x + 1[/tex], is given in slope-intercept form. The slope of that line is [tex]m_{1} = (-4)[/tex] while the [tex]y[/tex]-intercept of that line is [tex]b_{1} = 1[/tex].
Both [tex]m[/tex] and [tex]b[/tex] need to be found for the second line.
Start by finding the slope [tex]m_{2}[/tex] of the second line.
Make use of the fact that if two lines in a plane are perpendicular to one another, the product of their slopes would be [tex](-1)[/tex]. In other words, if a line with slope [tex]m_{1}[/tex] is perpendicular to a line with slope [tex]m_{2}[/tex], then [tex]m_{1}\, m_{2} = (-1)[/tex]. Rearrange to obtain [tex]m_{2} = (-1) / m_{1}[/tex].
In this question, since the slope of the first line is [tex]m_{1} = (-4)[/tex], the slope of the second line (perpendicular to the first line) would be [tex]m_{2} = (-1) / (-4) = (1/4)[/tex].
Thus, the equation of the second line would be of the form [tex]\displaystyle y = (1/4)\, x + b_{2}[/tex] for some constant [tex]b_{2}[/tex] that needs to be found.
Make use of the fact that the second line goes through the point [tex](-4,\, 1)[/tex] to find the value of [tex]b_{2}[/tex]. Since the point [tex](-4,\, 1)\![/tex] is on the second line, the equation of the second line should hold after substituting in [tex]x = (-4)[/tex] and [tex]y = 1[/tex]. That is:
[tex]1 = (1/4)\times (-4) + b_{2}[/tex].
Solve this equation for [tex]b_{2}[/tex]:
[tex]b_{2} = 2[/tex].
Therefore, the equation of the second line would be [tex]y = (1/4)\, x + 2[/tex].
Help help ASAP please
Answer:
y = -4x + 15
Step-by-step explanation:
slope of y = x/4 - 2 is 1/4
slope of line perpendicular to above line is -4
so y = -4x + b
use (4, -1)
-1 = -4(4) + b
b = 16 - 1 = 15
so
y = -4x + 15
How long does a missed payment on a mortgage stay on a consumer’s credit report?
A 2 years C 7 years
B 10 years D 5 years
Answer: C) 7 years
There's not much explanation other than I did an online search for the answer. Many sources I'm finding are saying "up to 7 years", which means that is the longest it will stay on the credit report.
You roll a six sided die. Find the probability of 1) event A rolling a 3.
2) event B rolling a 7 3) event C rolling a number less than 5.
Answer:
total sum (s)= 6
probability of getting a 3 = 3÷6
= 1÷2
Step-by-step explanation:
probability of getting a 7 =0÷7
=0
probability of getting less than 5 =4÷6
2÷3
Determine the cost of flooring a home office with carpet tiles, ceramic tiles, and laminate tiles. (Just flooring-not labor,tools,equipment,etc). Show all calculations. Include units with final and answers in space provided. Round to the nearest tenth if needed.
a) Carpet price $46.44 per box of 16 carpet tiles. Each tile 18"x 18"
Sold by the box only
b) Ceramic tile $2.98 for each individual tile. Each tile 12"x"12
Sold by the individual tile
c) Laminate cost $34.88 for a box that covers 17.5 square feet.
Sold by the box only
Question- 1.) How much flooring will be needed for the new office?
2.) Calculate the cost of flooring the new office with carpet tiles.
3.)Calculate the cost of flooring the new office with ceramic tiles
4.) Calculate the cost of flooring the new office with laminate flooring
Show all Work
(Please Help Thank you so much)
A hotel room cost $79 per night. Meg's family is getting 2 rooms for 5 nights for their trip.
What is the total hotel bill, without tax and fees?
A. 790
B. 880
C. 1056
D. 1120
AABC and ADEF are similar. Find the missing side length.
Answer:
/\ABC------/\DEF
the ratio of the the corresponding sites must be same
AB/AC=DE/DF
AB/30=4/5
AB=(4/5)30
AB=24
HOPE IT HELPED.
PLEASE MARK BRAINLIEST
Astronomers measure large distances in light-years. One light-year is the distance that light
can travel in one year, or approximately 5.88x10^12 miles. Suppose a star is 2.23x10^2 light-
years from Earth. In scientific notation, approximately how many miles is it?
A. 2.23x10^14
B. 1.31x10^14
C. 1.31X10^15
D. 5.88x10^12
Answer:
it's C
Step-by-step explanation:
Astronomers measure large distances in light-years. One light-year is the distance that light can travel in one year, or approximately 5.88\times 10^{12}5.88×1012 miles. Suppose a star is 2.23\times 10^22.23×102 light years from Earth.
To find : In scientific notation, how many miles away a star is from earth?
Solution :
One light-year is the distance that light can travel in one year is 5.88\times 10^{12}5.88×1012 miles.
In 2.23\times 10^22.23×102 lights year the distance is
=5.88\times 10^{12}\times 2.23\times 10^2=5.88×1012×2.23×102
=1.31124\times10^{15}=1.31124×1015
Therefore, Option C is correct.
PLS ANSWER AS SOON AS POSSIBLE
Step-by-step explanation:
[tex]36 - {b}^{2} - {c}^{2} + 2bc[/tex]
Factor out -1
[tex] - ( - 36 + {b}^{2} + {c}^{2} - 2bc[/tex]
[tex] -( (b + c) { }^{2} - 36[/tex]
[tex] - (b + c + 6)( b + c - 6)[/tex]
Use the number lines below to fill in an equivalent fraction.
1/4
What is 3/4 - 2/6
Subtracting Proper Fractions
Maya wants to show 28 as tens and ones . What are all the ways ?
Answer:
2 tens and 8 ones
Step-by-step explanation:
2 tens =20 , 8 ones = 8 . 20+8=28
Hope this helped
You and eight friends plan a surprise party. Each of you contributes the same amount of
money m for food. Their mom also contributes $20.
a. Write an algebraic expression for the total amount of money contributed for food.
b. Evaluate your expression if each person contributed $10.50
Answer:
a. 9m + 8×$20 = $340
b. 9×$10.50 + 8×$10.50 = $178.50
Step-by-step explanation:
Its self-explanatory
Are any two line segments always similar or not always similar
Answer:
➢ Line segments are congruent if they have the same length. However, they need not be parallel. They can be at any angle or orientation on the plane. ... If you drag any of the four endpoints, the other segment will change length to remain congruent with the one you are changing.
[tex]Into \: your Arms[/tex]
#CarryOnLearning
Answer:
No, they are not
Step-by-step explanation:
Line segments are congruent if they have the same length. However, they need not be parallel. They can be at any angle or orientation on the plane.
If you drag any of the four endpoints, the other segment will change length to remain congruent with the one you are changing.
answer this please? :)
Answer:
yes
Step-by-step explanation:
see the attachement