Answer:
B
Step-by-step explanation:
it is 64 units so 8 units long each
Answer:
B) (21, -14) and (21, -22)
Step-by-step explanation:
Given,
The area of the square = 64 square unit,
Let x be the side of the square,
[tex]\implies x^2 = 64[/tex]
[tex]\implies x = 8[/tex]
Hence, the side of the square = 8 unit,
⇒ The distance between the adjacent vertices in the square = 8 units,
By the distance formula,
The distance between (3, -35) and (3, -28) is,
[tex]\sqrt{(3-3)^2+(-28-(-35))^2[/tex]
[tex]=\sqrt{0+(-28+35)^2}[/tex]
[tex]=\sqrt{7^2}[/tex]
[tex]=7\neq 8[/tex]
Thus, (3, -35) and (3, -28) can not be the vertices of the square.
The distance between (21, -14) and (21, -22) is,
[tex]\sqrt{(21-21)^2+(-22-(-14))^2[/tex]
[tex]=\sqrt{0+(-22+14)^2}[/tex]
[tex]=\sqrt{8^2}[/tex]
[tex]=8[/tex]
Thus, (21, -14) and (21, -22) are the vertices of the square.
The distance between (32, -42) and (32, -7) is,
[tex]\sqrt{(32-32)^2+(-7-(-42))^2[/tex]
[tex]=\sqrt{0+(-7+42)^2}[/tex]
[tex]=\sqrt{35^2}[/tex]
[tex]=35\neq 8[/tex]
Thus, (32, -42) and (32, -7) can not be the vertices of the square.
The distance between (74, 19) and (82, 27) is,
[tex]\sqrt{(82-74)^2+(27-19)^2[/tex]
[tex]=\sqrt{8^2+8^2}[/tex]
[tex]=\sqrt{64+64}[/tex]
[tex]=\sqrt{128}[/tex]
[tex]=8\sqrt{2}\neq 8[/tex]
Thus, (74, 19) and (82, 27) can not be the vertices of the square.
Why do people save more when the Federal Bank sets a high interest rate on deposits? A. Spending on nonessential items decreases. B. Interest on savings can be earned. C. Financial institutions insist on a minimum balance. D. The unemployment rate goes down.
Answer: b
Step-by-step explanation:
The Kwans are saving for their daughter’s college education. If they deposit $12,000 in an account bearing 6.4% interest compounded continuously, how much will be in the account when Ann goes to college in 12 years? a. $12,768 c. $21,216.12 b. $25,865.41 d. $76,800
After 12 years there will be $25,865.41 in the bank account when Ann goes to college option (b) is correct.
What is compound interest?It is defined as the interest on the principal value or deposit and the interest which is gained on the principal value in the previous year.
We can calculate the compound interest using the below formula:
[tex]\rm A = P(1+\dfrac{r}{n})^{nt}[/tex]
Where A = Final amount
P = Principal amount
r = annual rate of interest
n = how many times interest is compounded per year
t = How long the money is deposited or borrowed (in years)
The formula for the compounded continuously:
[tex]\rm A = Pe^{rt}[/tex]
r = 6.4% = 0.064
t = 12
P = $12,0000
[tex]\rm A = 12,0000e^{0.064\times12}[/tex]
After solving:
A = $25,865.41
Thus, after 12 years there will be $25,865.41 in the bank account when Ann goes to college option (b) is correct.
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PLEASE HELP!!!
SOLVE FOR X ASAP
Answer:38
Step-by-step explanation:
Answer:
x = 1
Step-by-step explanation:
Since the triangle is right use Pythagoras' identity to solve for x
The square on the hypotenuse is equal to the sum of the squares on the other 2 sides.
The hypotenuse is the side opposite the right angle, thus
x² + 1² = ([tex]\sqrt{2}[/tex])²
x² + 1 = 2 ( subtract 1 from both sides )
x² = 1 ( take the square root of both sides )
x = [tex]\sqrt{1}[/tex] = 1
HELP ME ASAP!
(6.15x+0.24y)÷1.5+5.9x−1.6y
simplify it!
The simplification of the equation (6.15x + 0.24y / 1.5) + 5.9x - 1.6y is 10x - 2.16y/1.5
How to simplify equation?(6.15x + 0.24y / 1.5) + 5.9x - 1.6y
= 6.15x + 0.24y + 1.5(5.9x - 1.6y) / 1.5
= (6.15x + 0.24y + 8.85x - 2.4y) / 1.5
= (6.15x + 8.85x + 0.24y - 2.4y) / 1.5
= (15x - 2.16y) / 1.5
= 10x - 2.16y/1.5
Therefore, the answer to the equation is 10x - 2.16y/1.5
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square root of 6889 with work
Answer:
83
Step-by-step explanation:
A university conducted a study and determined that a college student walks an average of 2.4 miles a day and a college graduate walks an average of 1.8 miles per day. Which of the following is the best way to represent this data? -using a bar graph where one bar has a length of 2.4 and one bar has a length of 1.8 -using a cube with a side length of 2.4 and a cube with a side length of 1.8 -using a pie chart with one section labeled 1.8 and one section label 2.4 -using a square with a side length of 2.4 and a square with a side length of 1.8
Answer:
Using a bar graph where one bar has a length of 2.4 and one bar has a length of 1.8
Step-by-step explanation:
You use a bar graph to compare things between different groups, so it is the most appropriate one to use.
You use a pie chart to compare parts of a whole, so it would not be appropriate.
The graph should represent the relative sizes of the two values (24:18 or 1.33:1). Using a square or a cube would distort the relationship. The relative area of the squares would be 1.77:1 and that of the cubes would be 2.37:1.
Charts are used to represent data graphically.
The best way to represent the data is (a) using a bar graph where one bar has a length of 2.4 and one bar has a length of 1.8
The given parameters are:
[tex]\mathbf{Student = 2.4}[/tex]
[tex]\mathbf{Graduate = 1.8}[/tex]
Both data elements, are for different people.
So, it is best to use a bar chart.
Using a pie chart will imply that, the data elements are part of a whole data for a particular person.
Squares and cubes cannot be used at all.
Hence, the correct option is (a).
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3/4 times what equals 1/4
Final answer:
To find what multiplied by 3/4 equals 1/4, set up the equation 3/4 * x = 1/4 and solve for x, giving the answer x = 1/3.
Explanation:
This question demands basic understanding of multiplication and reciprocals.
The question asks, "3/4 times what equals 1/4?". To find the answer, we can set up the equation 3/4 * x = 1/4, where x is the unknown we are trying to find. Solving for x involves dividing both sides of the equation by 3/4 to isolate x.
Therefore, the equation simplifies to x = (1/4) / (3/4). Performing the division gives us x = 1/3. This means that 1/3 is the number you need to multiply by 3/4 to get 1/4.
To find what number multiplied by 3/4 equals 1/4, divide 1/4 by 3/4, which is the same as 1/4 times the reciprocal of 3/4 (4/3), resulting in 1/3.
To find out 3/4 times what equals 1/4, we are essentially looking for a number that when multiplied by 3/4 gives us 1/4. The mathematical operation we need to use is division since we want to find what 1/4 divided by 3/4 is. So, the equation we are solving is (1/4) ÷ (3/4).
When we divide fractions, we multiply by the reciprocal of the divisor. The reciprocal of 3/4 is 4/3. So, the calculation now is (1/4) × (4/3).
Multiplying the numerators and denominators separately, we get (1 × 4) / (4 × 3) which simplifies to 4/12. After simplification, 4/12 reduces to 1/3. Therefore, 3/4 times 1/3 equals 1/4.
Complete question is :
3/4 times is what equals 1/4?
25 POINTS PLEASE HELP
YOU CAN CHOOSE MORE THAN ONE
Select all the correct answers.
A survey of 30 students each from three different high schools was conducted to find the number of hours they spent every month on volunteer work. Based on the median values of the data sets, represented here as dot plots, which conclusions are true?
The students in school 2 generally spend more time doing volunteer work than the students in school 1.
The students in school 1 generally spend more time doing volunteer work than the students in school 2.
The students in school 1 generally spend more time doing volunteer work than the students in school 3.
The students in school 1 generally spend less time doing volunteer work than the students in school 3.
The students in school 3 generally spend more time doing volunteer work than the students in school 2.
From the information given, it is true to state that:
"The students in school 1 generally spend more time doing volunteer work than the students in school 2." (Option B)
What is a dot plot?In statistics, a dot plot, also known as a dot chart is a type of histogram or histogram-like chart that is used to represent data that is relatively small.
It is best used for indicating the statistical relationship between the data and its clusters, outliers, and gaps.
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School 2 students generally spend more time on volunteer work than School 1, while School 1 students tend to spend more time than School 3.
Based on the dot plots representing the number of hours spent on volunteer work by students from three different high schools, we can draw some conclusions about the median values of the data sets.
Firstly, comparing School 1 and School 2, it appears that students in School 2 generally spend more time doing volunteer work. This conclusion is supported by the higher frequency of dots in the higher hour range in School 2 compared to School 1.
Next, comparing School 1 and School 3, it seems that students in School 1 generally spend more time on volunteer work. The dot plot for School 1 shows a higher frequency of dots in the higher hour range compared to School 3.
In summary, students in School 2 generally spend more time doing volunteer work than those in School 1, while students in School 1 tend to spend more time on volunteer work than those in School 3.
What is the degree of the polynomial given below?
F(x)=2x^3-x^2+5x-3
A. 2
B. 5
C. 4
D. 3
Answer:
it is 3 i am pretty sure
Step-by-step explanation:
I believe the answer is 3
plzzzz answer!!! 20 points!!!
Two lines, A and B, are represented by the equations given below:
Line A: y = x – 6
Line B: y = 3x + 4
Which of the following shows the solution to the system of equations and explains why?
(–5, –11), because the point satisfies both equations
(–5, –11), because the point does not lie on any axis
(–3, –5), because the point satisfies one of the equations
(–3, –5), because the point lies between the two axes
ANSWER
(–5, –11), because the point satisfies both equations
EXPLANATION
The given equations are:
Line A: y = x – 6
Line B: y = 3x + 4
We substitute (-5,-11) into both equations.
Line A: -11 = -5– 6
This implies that,
-11=-11
This statement is true.
Line B: -11= 3(-5)+ 4
-11= -15+ 4
-11=-11
This is also true.
Since this point ,(&6,-11) satisfy both equations, it is their solution.
First-year students at a school must choose one each of 5 English classes, 4 history classes, 5 math classes, and 3 physical education classes. Find the total number of outcomes
Answer: 68 total outcomes
Final answer:
To find the total number of outcomes, we multiply the number of options for each class type using the fundamental counting principle, resulting in 5 × 4 × 5 × 3 = 300 total outcomes.
Explanation:
The question asks us to find the total number of outcomes for first-year students at a school who must choose one each of 5 English classes, 4 history classes, 5 math classes, and 3 physical education classes. To calculate the total number of outcomes, we use the fundamental counting principle, which states that if there are m ways to do one thing, and n ways to do another, then there are m × n ways of doing both.
In this scenario, the student can choose:
5 English classes
4 history classes
5 math classes
3 physical education classes
Applying the fundamental counting principle, we multiply the number of options for each subject:
5 (English) × 4 (History) × 5 (Math) × 3 (Physical Education) = 300 total outcomes.
The sum of the degree measures of any triangle is 180. In a particular isosceles triangle the degree measure of the vertex angle is 112. Find the measure of each base angle
Answer:
34
Step-by-step explanation:
Each of the base angles = x
x + x + 112 = 180 Subtract 112 from both sides. Simplify the left side.
2x + 112 - 112 = 180 - 112 Simplify
2x = 68 Divide by 2
2x/2 = 68/2 Simplify
x = 34
Each of the base angles = 34 degrees.
Solve the equation below for x.
-1/2(3x-4)=11
Answer:
x=-6
Step-by-step explanation:
You are given the equation
[tex]-\dfrac{1}{2}(3x-4)=11[/tex]
First, multiply it by 2 to get rid of fraction:
[tex]-(3x-4)=22[/tex]
Now open the brackets:
[tex]-3x+4=22[/tex]
Subtract 4 from both sides:
[tex]-3x+4-4=22-4\\ \\-3x=18[/tex]
Multiply it by -1:
[tex]3x=-18[/tex]
and divide by 3:
[tex]x=-6[/tex]
Answer:
[tex]\large\boxed{x=-6}[/tex]
Step-by-step explanation:
[tex]-\dfrac{1}{2}(3x-4)=11\qquad\text{multiply both sides by (-2)}\\\\(-2\!\!\!\!\1\diagup^1)\cdot\left(-\dfrac{1}{2\!\!\!\!\1\diagup_1}\right)(3x-4)=(-2)\cdot11\\\\3x-4=-22\qquad\text{add 4 to both sides}\\\\3x-4+4=-22+4\\\\3x=-18\qquad\text{divide both sides by 3}\\\\\dfrac{3x}{3}=-\dfrac{18}{3}\\\\x=-6[/tex]
24 is 0.4 of what number
Answer: 600
Step-by-step explanation:
We have, 4% × x = 24
or, 4 100 × x = 24
Multiplying both sides by 100 and dividing both sides by 4,
we have x = 24 × 100 4
x = 600
If you are using a calculator, simply enter 24×100÷4, which will give you the answer.
Find the x-intercept of the graph of the linear equation y=-1/2x+3
Answer:
x = 6
Step-by-step explanation:
To find the x- intercept let y = 0, that is
- [tex]\frac{1}{2}[/tex] x + 3 = 0 ( subtract 3 from both sides )
- [tex]\frac{1}{2}[/tex] x = - 3 ( multiply both sides by - 2 )
x = 6 ← value of x- intercept
Answer:
6
Step-by-step explanation:
got it right on edge
How long will it take you to ski a distance of 24 miles at a speed of 6 miles per 30 minutes? (Step by step please)
Answer:
4.8 minutes
Step-by-step explanation:
Time = Speed * Distance
Time = 6 mi / 30 min * 24 miles= 1 mi / 5 min * 24 miles = 0,2 mi / min * 24 = 4.8 minutes
Answer:
So if you know that you can complete 6 miles over the course of 30 minutes it is just matter of multipling 30 minutes times 4, this is becasue it takes 4 times your base distance and time to get to yur goal of 24 miles.
30 x 4 equal 120
which you divide by 60 (because you have 60 minutes in one hour)
so it is safe to say that it will take 2 hours of 120 minutes to ski a ditance of 24 miles at a speed of 6 miles per 30 minutes.
Hope this helps!
Please help me with this. TWO LINES MEET AT A POINT THAT IS ALSO THE ENDPOINT OF TWO RAY'S. SET UP AND SOLVE THE APPROPRIATE EQUATIONS FOR m AND N.
Answer:
m=47, n=52
Step-by-step explanation:
m is equal to 90-43 since 43+m is a right angle (straight angle 180 is composed of two right angles). n is equal to 90-38. If you solve of the missing angle not given a variable, you find n as well because opposite angles are congruent and have the same measure.
(x^2-2)^2-10(x^2-2)+21=0 find one value of x that is a solution to the equation
Answer:
x=3; x=-3; x=√5; x=-√5
Step-by-step explanation:
The equation can be simplified by treating (x^2 - 2) as y. Solving the quadratic equation for y results in y = 4 and y = 7. By substituting these back into the equation and solving for x, we find x = ±sqrt(6) and x = ±sqrt(9). Therefore, one possible solution for x is sqrt(6).
Explanation:The equation provided is a quadratic in the form of x. In this case, let's take: (x^2 - 2) = y. Therefore the equation can be rewritten as: y^2 - 10y + 21 = 0. In order to find the roots of the equation, we should use the quadratic formula: y = [10 ± sqrt((10)^2 - 4*1*21)] / (2*1), which gives us y = 4 and y = 7. Now we substitute back y = (x^2 - 2). This will form two more quadratic equations: x^2 - 2 = 4 and x^2 - 2 = 7. Solving these, we get x = ±sqrt(6) and x = ±sqrt(9). So, one value of x that is a solution to the equation could be sqrt(6).
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If line s and line t are parallel lines cut by transversal line r, what is the value of x?
x = 18
x cannot be determined from the information given
x = 33
x = 12
Answer:
Because s and t are parallel x=12
Step-by-step explanation:
To get this you have to solve for (4x-12)+120=180 solve for x
4x+12=60
4x=48
=12
The equation is written as 4x - 12 + 120 = 180. Then the value of the variable 'x' will be 18. Then the correct option is A.
What is an angle?The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360°.
Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.
The sum of the angle (4x - 12)° and (120)° will be equal to 180°. Then the equation is given as,
4x - 12 + 120 = 180
Simplify the equation, then we have
4x - 12 + 120 = 180
4x = 72
x = 72 / 4
x = 18
The equation is written as 4x - 12 + 120 = 180. Then the value of the variable 'x' will be 18. Then the correct option is A.
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A tray of cake samples contains a variety of flavors.
chocolate
33
vanilla
9
strawberry
3
What is the probability that a randomly selected piece of cake will be vanilla?
Simplify your answer and write it as a fraction or whole number.
p( vanilla)
The total pieces of cake equal 45. 9 pieces are vanilla. This gives the fraction 9/45 which can be simplified to 1/5. P(vanilla)=1/5
Is -2 +-2 A. Positive B. Negative C Both or D None of the above
Answer:
B
Step-by-step explanation:
If I have two dollars of debt (negative) and add 2 more dollars of debt (negative), I now owe 4 dollars in debt (negative).
-2+-2=-4
Answer:
B.) Negative 4
Step-by-step explanation:
A negative plus a negative equales a negative, beacause you aren't adding a positive to cancle out some of the numbers. your just adding more negative.
A steel pipe 100 cm long has an outside diameter of 2 cm and an inside diameter of 1.8 cm. If thee density of the steel is 7.8 grams per cm^3, what is the mass of the pipe to the nearest gram?
Answer:
The mass of the pipe is [tex]465\ g[/tex]
Step-by-step explanation:
step 1
Find the volume of the steel pipe
The volume is equal to the area of outside circle minus the area of inside circle, multiplied by the length of the pipe
so
[tex]V=\pi [r2^{2}-r1^{2}]L[/tex]
we have
[tex]r2=2/2=1\ cm[/tex] ---> the radius is half the diameter
[tex]r1=1.8/2=0.9\ cm[/tex] ---> the radius is half the diameter
[tex]L=100\ cm[/tex]
[tex]\pi=3.14[/tex]
substitute
[tex]V=(3.14)[1^{2}-0.9^{2}](100)=59.66\ cm^{3}[/tex]
step 2
Find the mass
The mass is equal to the density multiplied by the volume
so
[tex]m=7.8(59.66)=465\ g[/tex]
Answer:
466
Step-by-step explanation:
Which list is in order from least to greatest? A) 9.4 * 10^-8, 9.25 * 10^-6, 2.5 * 10^3, 7* 10^3 B) 2.5 *10^3, 7 * 10^3, 9.25 * 10^-6, 9.4 * 10^-8. C) 9.25 * 10^-6, 9.4 * 10^-8, 7 * 10^3, 2.5 * 10^3 D) 9.4 * 10^-8, 9.25 * 10^-6, 7 * 10^3, 2.5 * 10^3
ANSWER
A) 9.4 * 10^-8, 9.25 * 10^-6, 2.5 * 10^3, 7* 10^3
EXPLANATION
The numbers are given in standard form.
The first criteria we will use to order them is the exponents.
The bigger the exponents the bigger the number.
The second criteria is that, if the exponents of any two numbers are the same, then we use the numbers multiplying the powers of 10 to order.
[tex]9.4 * 10^{-8} \: < \: 9.25 * 10^{-6} \: < \: 2.5 * 10^3 \: < \: 7* 10^3[/tex]
The correct choice is A.
Answer:
Option A. [tex]9.4\times 10^{-8}< 9.25\times 10^{-6}< 2.5\times 10^{3}<7\times 10^{3}[/tex]
Step-by-step explanation:
The given numbers are [tex]9.4\times 10^{-8}, 9.25\times 10^{-6}, 2.5\times 10^{3},7\times 10^{3}[/tex].
These are numbers written in scientific notation.
To identify the order of the numbers from least to greatest we will convert the numbers into the standard from.
[tex]9.4\times 10^{-8}[/tex] = 0.000000094
[tex]9.25\times 10^{-6}[/tex] = 0.00000925
[tex]2.5\times 10^{3}[/tex] = 2500
[tex]7\times 10^{3}[/tex] = 7000
Now we can arrange then from least to greatest.
0.000000094 < 0.00000925 < 2500 < 7000
OR
[tex]9.4\times 10^{-8}< 9.25\times 10^{-6}< 2.5\times 10^{3}<7\times 10^{3}[/tex]
Option A. is the answer.
A real estate agent received a 6% commission on the selling price of a house. If his commission was $8,880, what was the selling price of the house?
Answer:
6% x = 8,880 : x = selling price of house.
x = $148,000 : solve for x
Step-by-step explanation:
The selling price of the house can be calculated by dividing the commission ($8,880) by the commission rate (0.06). This gives a selling price of $148,000.
Explanation:To solve this problem, you need to understand that the 6% commission the real estate agent received is based on the selling price of the house. You can find the selling price by dividing the commission by the percentage commission expressed as a decimal.
Here's the step-by-step solution:
Convert the 6% commission rate to a decimal by dividing 6 by 100, which gives 0.06.Next, divide the commission amount ($8,880) by the commission rate (0.06). Using this calculation, $8,880 / 0.06, we find that the selling price of the house is $148,000.So, the selling price of the house on which the agent earned an $8,880 commission at a rate of 6% was $148,000.
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which equation best fits these data? PLEASE HELP
Answer:
C
Step-by-step explanation:
Use a quadratic equation regression calculator.
Plugging in all the points, the equation should come somewhere close to
[tex]y=-0.32x^{2} -1.26x+15.81[/tex]
Which is answer choice C.
Answer:
The correct option is C.
Step-by-step explanation:
Answer:
The required quadratic regression model is [tex]y=x^2-2x-3[/tex].
Step-by-step explanation:
The given data points are (-6,12), (-4,15), (-3,17), (-1,17), (1,15), (2,11), (3,9), (4,6).
From the graph it is clear that the given data forms a U-shaped curve. It means we have to find the quadratic regression model.
The general form of quadratic regression model is
[tex]y=ax^2+bx+c[/tex]
Using technology we get,
[tex]a=-0.32,b=-1.26,c=15.81[/tex]
The required quadratic regression model is
[tex]y=-0.32x^2-1.26x+15.81[/tex]
Therefore the correct option is C.
What is the value of b in the equation below? 9^-8 x 9^-2 = a^b
Answer:
b= -10
Step-by-step explanation:
9^ -8 * 9^ -2
We know that a^b * a^c = a^ (b+c)
9^ (-8+-2)
9^ -10
We want it in the form a^b
a=9
b= -10
Answer:
-10
Step-by-step explanation:
1st: the
2nd: expect
3rd: said
last step: so
please help Use the model to solve for x.
A)
no solution
B)
x = 3
C)
x = -3
D)
x = -
3
2
Answer:
A) no solutionStep-by-step explanation:
x + 1 = x - 1 - 1
x + 1 = x - 2 subtract x from both sides
x - x + 1 = x - x - 2
1 = -2 FALSE
Three more than twice the sum of a number and half the number equals 105. Which equation models this relationship?
A 2(x+1/2x)+3=105
B 2x+1/2x+3=105
C 2x+3=1/2x+105
D 2(x+3)=1/2x+105
it's a.
three more is +3 and it equals 105
that already eliminates c and d
next it says twice the sum of a number and half the number
Answer:
a
Step-by-step explanation:
Which is the operation to do second based on the order of operations?
4+5×(7−3)
A. Subtract 3 from 7
B. Add 4 to the product of 5 and the difference of 7 and 3
C. Multiply 5 by the difference of 7 and 3
D. Multiply 7 by the sum of 4 and 5
The answer to this is C.
Round 3.75 to the tenths place
Answer:3.8
Step-by-step explanation: 5 or up you round up so you round up so it is 3.8
Answer:
3.8
Step-by-step explanation:
if the hundredth place is 5 or greater then turn the tenth place to 8 so 3.8