Answer:
Step-by-step explanation:
we know that
in a right triangle
if sin A= cos B
then
angle A and angle B are complementary angles
so A+B=90
therefore
(7x-15)+(3x+5)=90-----> 10x-10=90----> 10x=100----> x=10°
so
7x-15------> 7*10-15----> 55°
3x+5------> 3*10+5----> 35°
we know that
β < α
therefore
the answer is
β =35°
α=55°
Answer:
34
Step-by-step explanation:
Thats the answer o usatest prep
Apex Help!!!! At the beginning of year 1, Gracie invest $350 at annual simple interest rate of 4%. She makes no deposits to or withdrawals from the account
It's B A(n)= 350 + (n - 1) (0.04 · 350); $504.00
Answer:
Option B.
Step-by-step explanation:
Gracie invest $350 at the beginning of the year 1 at annual simple interest rate of 4%.
the balance at the beginning of the year 12. Interest will be calculated for 11 years.
Formula for simple interest : A = P(1 + rt)
By putting the value : A = 350(1 + 0.04 × 11)
A = 350 ( 1.44 ) = $504.00
So the best answer would be option B.
Which of the following arcs are congruent in the circle below?
D) Arc wx and arc yz is the correct answer because both arcs are equal to 27
Answer:
Option D is correct.
Step-by-step explanation:
Arcs are said to be equal if it subtends equal angles at the center
here we can see that arcs WX and ZY subtends equal angle and its measure is 27 degrees.
therefore option D is correct answer
Since we are not given the angles subtended by WY and XZ in the center
so we cannot say for option A
Likewise we cannot say for rest of the option.
If you are going to use the SAS postulate to prove these two triangles congruent what additional information do you need
Answer:
Option D. ET=IT
Step-by-step explanation:
we know that
The Side Angle Side postulate (SAS) states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then these two triangles are congruent
In this problem
the included angle ∠ETK of triangle TEK is congruent with the included angle ∠KTI of triangle TIK
the side KT is a common side both triangles
therefore
ET must be equal to IT to prove that triangles TEK and TIK are congruent by SAS postulate
What's the least amount 0.146, 2.0102, 0.45, 1.09, 2.001
The least amount would be 0.146 because the tenths digits is the smallest.
The least amount among the given different amounts is 0.146
What is least amount of something?Least amount of something means the smallest amount or number.
How to find the least number or amount among the list of numbers?To find the least number or amount among the list of numbers we first go through the whole list of numbers and compare their values one after the other. And we arrange these numbers or amount in ascending order and find the least one.
According to the given question
We have different amounts
0.146, 2.0102, 0.45, 1.09, 2.001
For finding the least amount, arrange all the given amount in the ascending order.
So, the required ascending order is
0.146, 0.45, 1.09, 2.001, 2.0102
Hence, the least amount among the given different amounts is 0.146.
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Two groups of workers are painting a bridge in the bay. The first group is responsible for painting the north side of the bridge, and the second group is responsible for painting the south side of the bridge. The first group has already painted 2 kilometers of the bridge and is painting 2 additional kilometers per day. The second group has already painted 5 kilometers of the bridge and is painting 1 additional kilometer per day. When the two groups have painted the same amount of the bridge, how much of the bridge will they each have painted?
Answer:
They will each have painted 8 km. This goal will be met on Day 4.
Step-by-step explanation:
Group A | Group B
Start: 2 | Start: 5 Day 1
2 + 2 = 4 | 5 + 1 = 6 Day 2
4 + 2 = 6 | 6 + 1 = 7 Day 3
6 + 2 = 8 | 7 + 1 = 8 Day 4
The first group and second group of workers will each have painted 8 kilometers of the bridge after 3 days.
Explanation:This question is related to the concept of linear equation in one variable. To solve such a problem, we typically set up an equation that relates the two groups and the amount they have painted to find out when they have painted an equal amount.
The equation representing the painting work of the first group is: 2 + 2d = x, where d is the number of days and x is the total distance painted. For the second group, the equation is 5 + d = x. We can set up these equations because each new day adds certain kilometers to the existing painted distance.
To find when these two equations are equal, we can simply equate them: 2 + 2d = 5 + d. Solving this equation, we get d = 3 days. Substituting d = 3 into either of the group's equations, we get x = 8 kilometers.
So, after 3 days, both groups would have painted 8 kilometers each.
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What is the equation of the line that passes through the points (2,-1) and (6,1)?
The answer is y=1/2x-2
List possible outcomes
Answer:
2. A. H-red, H-blue, H-green, H-yellow, T-yellow, T-green, T-blue, T-red
3. 18
Step-by-step explanation:
2. Flipping a coin and spinning a 4-color spinner.
There are two possible outcomes for the coin: heads or tails (H or T).
There are still 4 possibilities for the spinner: red, blue, green and yellow
Since both are independent, you multiply the possible outcomes of each event, so 2 * 4 = 8 possible outcomes.
To list them all, take each possible outcome on one item (coin or spinner), and match it with all the possible outcomes of the other item.
So answer is A. H-red, H-blue, H-green, H-yellow, T-yellow, T-green, T-blue, T-red
3. Lunch combinations
You have 2 sandwiches, 3 sides and 3 beverages. How many different lunches can you make picking one of each?
As in the problem above, these possible outcomes are independent (choosing one specific sandwich has no impact on the side or the beverage).
So, to count all the possible outcomes, you just have to multiply the possible outcomes of each item, so
L = 2 sandwiches x 3 sides x 3 beverages = 18 possible lunches
Solve -2(2x+5) -3(x-1)
The answer is:
[tex]-2(2x+5)-3(x-1)=-7x-7\\[/tex]
Why?To solve the problem, we need to perform the operations and then, add like terms.
We need to apply the distributive property, which is defined by the following way:
[tex]a(b+c)=ab+ac[/tex]
Also, we need to remember how to add like terms. Like terms are terms that share the same exponent and the same variable, for example:
[tex]3x+5x+x^{2}=8x+x^{2}[/tex]
We were able to add only the first two terms since they are like terms, both are sharing the same exponent and the same variable.
So, we are given the expression:
[tex]-2(2x+5)-3(x-1)[/tex]
Then, solving we have:
[tex]-2(2x+5)-3(x-1)=-4x-10-(3x-3)\\\\-4x-10-(3x-3)=-4x-10-3x+3\\\\-4x-10-3x+3=-4x-3x-10+3\\\\-4x-3x-10+3=-7x-7[/tex]
Hence, we have that the answer is:
[tex]-2(2x+5)-3(x-1)=-7x-7\\[/tex]
Have a nice day!
A rectangular prism has a length of 8 in., a width of 4 in., and a height of 2 1/4 in. The prism is filled with cubes that have edge lengths of 14 in. How many cubes are needed to fill the rectangular prism? Enter your answer in the box. To fill the rectangular prism, cubes are needed.
It is not possible to fill a smaller rectangular prism with larger 14-inch cubes.
However, there is a typo in the question because the cubes with an edge length of 14 inches cannot fit inside a rectangular prism of smaller dimensions.
Hence, it is impossible to fill the rectangular prism with cubes of 14-inch edge lengths.
Help please I don’t understand probability and need the correct answers to these questions.
Answer:
1) = 0.175
2) = 0.244
3) = 0.168
Step-by-step explanation:
Experimental, not theoretical, so we use the results table.
1. P(3 n Tails) = 62/(53 + 65 + 49 + 71 + 54 + 62) = 0.175
2. P(Woman n Up) = 39/(36 + 43 + 39 + 42) = 0.244
3. P(Tuna n Wheat Bread) = 23/(22 + 24 + 21 + 22 + 25 + 23) = 0.168
Linda Young opened up a computer service company. To pay for start up cost Linda borrowed $79,000 from a bank at 15% for 1 year. Find the interest for the year
Interest=Principal×Rate×Time
I=PRT/100
I= 79000×15×1
100
I= 1185000
100
I= $11850
To confirm
11850/79000 ÷ 100
= 0.5 ×100
= 15% (rate)
The interest of one year is $11850.
What is simple interest?
easy interest is based on the essential amount of a loan or the primary deposit in a savings account.
calculation:-
Amount of money borrowed by Linda = $79000
rate of interest =15%
Interest amount= $79000*15/100
The interest of the year =$11850
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The product of 43 x 6 can be broken down into expanded
form.
What is the missing expression?
43 x 6
= (40 6) + (?)
3x6
6x6
40 x 1
40 x 3
Answer:3*6
Step-by-step explanation: It is (40*6)+(3*6) you have to break it down
Find the value of x.
Answer:
x=60
Step-by-step explanation:
As the sides of the triangle are doubled (21 to 42 and 44 to 88) that means that the side of 30 is doubled to 60
Answer:
x=60
Step-by-step explanation:
Express the difference in the simplest form; 3t^2/5-4t^2/15
Answer:
t^2/3
Step-by-step explanation:
Sue danced for 15.5 minutes.Allie danced for 23.25 minutes. Carol danced for 8 minutes and 12 seconds less than Sue and Allie combined. How much time in minutes and seconds fed the girls dance altogether
Answer:69.38
Step-by-step explanation: Sue = 15.5 allie = 23.25 carol = 15.5+32.25 - 8.12 2. 15.5+32.25=38.75-8.12= 30.63 now all together 23.25+15.5+30.63= 69.38
The girls danced for a total of 30 minutes and 33 seconds.
First, we need to calculate the total time Sue and Allie danced combined:
Sue danced for 15.5 minutes, which can be written as [tex]\(\frac{155}{10}\)[/tex] minutes.
Allie danced for 23.25 minutes, which can be written as [tex]\(\frac{2325}{100}\)[/tex] minutes.
To combine these times, we need a common denominator, which is 100:
Sue's time in minutes: [tex]\(\frac{155 \times 10}{100} = \frac{1550}{100}\)[/tex]
Allie's time in minutes: [tex]\(\frac{2325}{100}\)[/tex]
Now we add Sue's and Allie's times:
[tex]\(\frac{1550}{100} + \frac{2325}{100} = \frac{3875}{100}\)[/tex]
Converting this back to mixed numbers:
[tex]\(\frac{3875}{100} = 38\)[/tex] minutes and [tex]\(\frac{75}{100}\)[/tex] minutes, which is 45 seconds.
Now, Carol danced for 8 minutes and 12 seconds less than the combined time of Sue and Allie. We need to subtract this time from the total time Sue and Allie danced:
[tex]\(38\)[/tex] minutes and [tex]\(45\)[/tex] seconds [tex]\(-\) \(8\)[/tex] minutes and [tex]\(12\)[/tex] seconds.
Subtracting the minutes:
[tex]\(38 - 8 = 30\)[/tex] minutes.
Subtracting the seconds:
[tex]\(45 - 12 = 33\)[/tex] seconds.
Therefore, Carol danced for 30 minutes and 33 seconds. Since Sue and Allie's combined time was 38 minutes and 45 seconds, and Carol danced for 8 minutes and 12 seconds less, the total time the girls danced altogether is:
[tex]\(38\)[/tex] minutes and [tex]\(45\)[/tex] seconds [tex]\(-\) \(8\)[/tex] minutes and [tex]\(12\)[/tex] seconds [tex]\(=\) \(30\)[/tex] minutes and [tex]\(33\)[/tex] seconds.
Thus, the girls danced for a total of 30 minutes and 33 seconds.
Matt is cutting quilt squares measuring 3 inches on each side he wants to use them to make a rectangular wall hanging measuring 1 yard by 2/1/2 feet how many quilt squares does he need
The answer is:
Matt will need 120 quilt squares.
Why?To solve the problem, we need to calculate the area of the wall and then, calculate how many quilt squares are needed.
We know that the wall measures 1 yard and 2 1/2 feet, also we know that the quilt squares measures 3 inches.
First, we need to conver the units:
So, converting we have that:
[tex]1yard=36inches[/tex]
Also,
[tex]1feet=12inches[/tex]
[tex]2.5*1feet=2.5*12inches[/tex]
[tex]2.5feet=30inches[/tex]
For the wall:
Calculating the area of the wall, we have:
[tex]Area_{rectangle}=base*height\\\\Area_{rectangle}=36inch*30inch=1080inch^{2}[/tex]
For the quilt squares:
Calculating the area of the quilt square, we have:
[tex]Area_{square}=side*side\\\\Area_{square}=3inch*3inch=9inch^{2}[/tex]
Therefore, to calculate how many quilt squares are needed, we need to use the following equation:
[tex]QuitSquaresNeeded=\frac{Area_{rectangle}}{Area_{square}}\\\\QuitSquaresNeeded=\frac{1080inch^{2}}{9inch^{2}}=120[/tex]
Hence, we have that Matt will need 120 quilt squares.
Have a nice day!
Answer:240
Step-by-step explanation:
i got this answer right on my school
please help me i’m very confused
The ratio of dry rice to water is 1 to 2. This means that water is two times more than dry rice. Since the chef uses 9.5 cups of dry rice, the chef needs 19 cups of water.
You can check by using fractions. 9.5 / 19 in simplified form is 1/2, which is 1:2 in ratio.
It would be 9.5:19 just multiply 9.5 by 2
Which set of fractions is ordered from least to greatest?
A) 5/8, 8/12, 3/4
B) 8/12, 5/8, 3/4
C) 3/4, 5/8, 8/12
D) 5/8, 3/4, 8/12
Answer:
a
Step-by-step explanation:
math
5/8, 8/12, and 3/4 are ordered from least to greatest.
What is ascending order of fractions?Write all the fractions so that they have a common denominator in order to arrange them in ascending order. By comparing the numerators and sorting the fractions, determine which fraction is the smallest. Rewrite the numbers in the order of size that they appear in the question.
Given
5/8, 8/12, 3/4
Least common multiple of 8, 4, and 12 is 24
[tex]\frac{5*3}{8*3} , \frac{8*2}{12*2} ,\frac{3*6}{4*6} \\\\\frac{15}{24} , \frac{16}{24} .\frac{18}{24}[/tex]
therefore, 5/8, 8/12, and 3/4 are ordered from least to greatest
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a model rocket is launched from a roof into a large field the path of the rocket can be modeled by the equation Y equals -0.05x^2 + 9.6 x + 5.4 where X is the horizontal distance in meters from the starting point on the roof and y is the height in meters of the rocket above the ground how far horizontally from its starting point will the rocket land round your answer to the nearest hundredth
•82.03 m
•6.50 m
• 90.00 m
• 88.53 m
The answer to this question is going to be 88.53 because you shift it horizontally
Answer:
it's 160 or 160. 56
Step-by-step explanation:
since you want the height horizontally from the starting height, and that height was 5.4 metres,
-.06x^2 + 9.6x + 5.4 = 5.4
the 5.4 drops out, so
x(-.06x + 9.6) = 0
x = 0 , the starting time
or
x = 9.6/.06 = 160
it will land after 160 m
what is perfect square trinomials
(x+4)^2=
Answer:
x² + 8x + 16
Step-by-step explanation:
(x + 4)² = (x + 4)(x + 4)
Each term in the second parenthesis is multiplied by each term in the first parenthesis, that is
x(x + 4) + 4(x + 4) ← distribute both parenthesis
= x² + 4x + 4x + 16 ← collect like terms
= x² + 8x + 16 ← perfect square trinomial
What is the probability that a vehicle is white?
Answer:
B. 0.22
Step-by-step explanation:
8/36 = 0.2222
B is the correct answer
Sara has a circular fence around her dog house. Each day when she comes home from
school the dog runs exactly three laps around his pen before he is calm enough to be
petted. If the radius of his pen is 12 meters, how far does her dog run?
Answer needs to be explained
WILL GIVE BRAINLYIST
Answer:
226.2 feet
Step-by-step explanation:
The fence around the dog's house is a circle, with a radius of 12 meters.
To calculate the distance the dog runs, we need to find the circumference of that circle, which is given by the formula:
C = 2 π r, since we know r, the calculation is easy:
C = 2 π 12 = 24 π = 75.4 feet.
The dog makes three laps around the circle before calming down... so he runs 3 times 75.4 feet.
Dogs run = 3 x 75.4 ft = 226.2 feet
factor z^2 - 3z - 18
Answer:
(z-6)(z+3)
Step-by-step explanation:
Answer:
The factored form of the given expression is (z-6)(z+3).
Step-by-step explanation:
The given expression is
[tex]z^2-3z-18[/tex]
The middle term can by written a -6z+3z.
[tex]z^2-6z+3z-18[/tex]
[tex]z(z-6)+3(z-6)[/tex]
[tex](z-6)(z+3)[/tex]
Therefore the factored form of the given expression is (z-6)(z+3).
Joy is planning to purchase a sweater that costs $30 dollars at her local department store. The sweaters are on sale for 20% off.
Which steps are needed to find the sale price of the sweater?
A. Convert the percent to its decimal equivalent. Multiply the decimal by the original amount to find the discount.
B. Convert the percent to its decimal equivalent. Divide the decimal by the original amount to find the discount. Subtract the discount from the original amount.
C. Convert the percent to its decimal equivalent. Multiply the decimal by the original amount to find the discount. Add the discount to the original amount.
D. Convert the percent to its decimal equivalent. Multiply the decimal by the original amount to find the discount. Subtract the discount from the original amount.
To find the sale price of a sweater, convert the discount percentage to a decimal, multiply by the original price to get the discount amount, and subtract this from the original price. So correct answer is B.
The correct steps needed to find the sale price of the sweater that Joy is planning to purchase are as follows:
Convert the percent discount to its decimal equivalent.
Multiply the decimal by the original amount to find the discount amount.
Subtract the discount amount from the original amount to determine the sale price.
Devon made a scale drawing of a triangle. He used a scale factor 1/4 to draw the new triangle. How does each side of the new triangle compare to the original?
Answer:
The sides of the new triangle compared to the original are 4 times smaller.
Step-by-step explanation:
we know that
If two figures are similar, then the ratio of its corresponding sides is proportional and this ratio is called the scale factor
Let
z-----> the scale factor
x----> the corresponding side of new triangle
y----> the corresponding side of the original triangle
[tex]z=\frac{x}{y}[/tex]
we have
[tex]z=\frac{1}{4}[/tex]
substitute
[tex]\frac{1}{4}=\frac{x}{y}[/tex]
[tex]x=\frac{1}{4}y[/tex]
therefore
The sides of the new triangle compared to the original are 4 times smaller.
Answer:
C
Step-by-step explanation:
use the quadratic formula to solve the equation 4x²-x+3=0
Answer:
[tex]x=\frac{1+ \sqrt{47}i}{8}[/tex] and [tex]x=\frac{1 -\sqrt{47}i}{8}[/tex]
Step-by-step explanation:
Given quadratic equation is [tex]4x^2-x+3=0[/tex].
Compare with [tex]ax^2+bx+c=0[/tex], we get:
a=4, b=-1, c=3
Now plug these values into quadratic formula :
[tex]x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}[/tex]
[tex]x=\frac{-\left(-1\right) \pm \sqrt{\left(-1\right)^2-4\left(4\right)\left(3\right)}}{2\left(4\right)}[/tex]
[tex]x=\frac{1 \pm \sqrt{1-48}}{8}[/tex]
[tex]x=\frac{1 \pm \sqrt{-47}}{8}[/tex]
[tex]x=\frac{1 \pm \sqrt{47}i}{8}[/tex]
Hence final answer is
[tex]x=\frac{1+ \sqrt{47}i}{8}[/tex] and [tex]x=\frac{1 -\sqrt{47}i}{8}[/tex]
Answer:
Solution of given quadratic equation,
x = [1 + 6.86i]/8 or x = [1 - 6.86i]/8
Step-by-step explanation:
Points to remember
Solution of a quadratic equation ax² + bx + c = 0
x = [-b ± √(b² - 4ac)]/2a
It is given a quadratic equation, 4x²-x+3=0
To find the solution using quadratic formula
Here a = 4, b = -1 and c = 3
We have,
x = [-b ± √(b² - 4ac)]/2a
x = [--1 ± √((-1)² - 4*4*3)]/2*4
= [1 ± √(1 - 48)]/8
= [1 ± √(-47)]/8
= [1 ± 6.86i]/8
x = [1 + 6.86i]/8 or
x = [1 - 6.86i]/8
Chuck puts $900,000 into an account that earns 5% APR compounded annually how much money will chuck earn each year in interest
Answer:
45,000
Step-by-step explanation:
Apex is the source
Answer: the answer is $ 45,000 APEX
What Is The Value Of 12 Divided By 6 2/3
Answer:9/5
Step-by-step explanation:
Hi there, hope this helps you. Have a great day! :)
Answer:
1 4/5
Step-by-step explanation:
1. Convert your mixed numbers to fractions. Your equation will become:
[tex]\frac{12}{1}[/tex] / [tex]\frac{2}{3}[/tex]
2. Apply the fractions formula for division.
[tex]\frac{12 x 3}{ 1 x 20}[/tex]
3. Solve the fraction formula for division.
You'll get [tex]\frac{36}{20}[/tex]
4. Simplify. Your final answer is [tex]1 \frac{4}{5}[/tex]
solve for X
(5x-2)^2=17
Answer:
hello : x = 2 +√17 or x = 2 -√17
Step-by-step explanation:
(5x-2)^2=17
5x-2 = √17 or 5x-2 = - √17
x = 2 +√17 or x = 2 -√17
which function has the greatest y- intercept? A. f(x)= 3x) B. 2x+3y=12 ) C. the line that has a slope of 2 and passes through (-1,-4) D. a graph
Answer:
#4
Step-by-step explanation:
1) The y intercept is 0.
2) Convert to slope-intercept form:
2x + 3y = 12
3y = -2x + 12
y = -2/3 x + 4
So the y-intercept is 4.
3) Write in point-slope form:
y + 4 = 2 (x - 1)
Now convert to slope-intercept form:
y + 4 = 2x - 2
y = 2x - 6
So the y-intercept is -6.
4) The y-intercept is 5.
So of the four lines, #4 has the largest y-intercept.
Answer:
[tex]\boxed{\text{(4) The graph}}[/tex]
Step-by-step explanation:
The question is asking, which function has the greatest value when x = 0?
We must evaluate f(0) for each one.
(1) ƒ(x) = 3x
f(0) = 3 × 0 = 0
(2) 2x + 3y = 12
Let x = 0.
2 × 0 + 3y = 12
0 + 3y = 12
3y = 12
y = 4
(3) The line
The line has a slope of 2, and y= -4 when x = 1.
y increases by 2 when x increases by 1.
For the same reason, y decreases by 2 when x decreases by 1.
Thus, when x decreases from 1 to 0, y decreases from -4 to -6.
f(0) = -6.
(4) The graph
The graph has a y-intercept at y = 5, so,
f(0) = 5.
[tex]\boxed{\textbf{The graph}}[/tex] has the greatest y-intercept.