Answer:
x = 9
Step-by-step explanation:
x+3=2x-6
3=2x-x-6
9=x
The value of the x for the figure ABCD is 9.
What are quadrilaterals?A closed quadrilateral has four sides, four vertices, and four angles. It is a form of a polygon. In order to create it, four non-collinear points are joined. Quadrilaterals always have a total internal angle of 360 degrees.
Given the quadrilateral ABCD and opposite sides are parallel,
AD ║ BC and AB ║ CD
since the opposite sides of the quadrilateral are parallel so the quadrilateral is a parallelogram,
so AB = CD
AB = x + 3 and CD = 2x - 6
x + 3 = 2x - 6
2x - x = 3 + 6
x = 9
Hence the value of x is 9.
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What is the vertex of the graph of the function y=(x+2)^2?
Answer:(2,0)
Step-by-step explanation:
4 1/2 −5 1/3 ÷(20x−14 2/3 )=1 5/6
Investors buy a studio apartment for $ 120,000. Of this amount, they have a down payment of $ 36,000. Their down payment is what percent of the purchase price? What percent of the purchase price would a $42,000 down payment be?
Answer:
[tex]\$ 36000\ down\ payment\ is=30\%\\\\\$ 42000\ down\ payment\ is=35\%[/tex]
Step-by-step explanation:
[tex]Purchase\ price=\$ 120000\\\\[/tex]
[tex]when\ down\ payment=\$ 36000\\\\percentage\ down\ payment=\frac{down\ payment}{total\ amount}\times 100\\\\percentage\ down\ payment=\frac{36000}{120000}\times 100\\\\percentage\ down\ payment=0.3\times 100=30\%[/tex]
[tex]when\ down\ payment=\$ 42000\\\\percentage\ down\ payment=\frac{down\ payment}{total\ amount}\times 100\\\\percentage\ down\ payment=\frac{42000}{120000}\times 100\\\\percentage\ down\ payment=0.35\times 100=35\%[/tex]
Final answer:
A $36,000 down payment is 30% of the $120,000 purchase price. A $42,000 down payment would be 35% of the purchase price.
Explanation:
To calculate what percent the down payment is of the purchase price, we use the formula:
(Down Payment / Purchase Price) x 100 = Percentage of Purchase Price
For the initial $36,000 down payment:
Divide $36,000 by the purchase price of $120,000 to get 0.3.
Multiply 0.3 by 100 to get 30%.
Therefore, a $36,000 down payment is 30% of the $120,000 purchase price.
For a $42,000 down payment:
Divide $42,000 by the purchase price of $120,000 to get 0.35.
Multiply 0.35 by 100 to get 35%.
A $42,000 down payment would be 35% of the purchase price.
How does the coefficient of a affect the way the parabola opens
Answer: If the x is squared, the parabola is vertical (opens up or down). If the y is squared, it is horizontal (opens left or right). If a is positive, the parabola opens up or to the right. If it is negative, it opens down or to the left.
Step-by-step explanation:
Answer:
If the y is squared, the parabola is horizontal. If the x is squared, the parabola is vertical. If it's negative the parabola opens down or to the left. If it's positive the parabola opens up or to the right.
Step-by-step explanation:
edge 2021
A basketball player shoots a basketball with an initial velocity of 15ft/sec. The ball is released from an initial height of 6.5 feet. The function h(t)=-16t^2+v0t+h0 models the height,in feet, of an object after t seconds. v0 is the initial initial height of the object
part one right function that models the height of the basketball use your function to answer part 2 through 4
part 2 how long does it take for the basketball to hit the ground round your answer to the nearest hundredth show all your work
part 3 when does the basketball reaches maximum height round your number to the nearest hundredth show all your work and explain your answer
what is the maximum height of the basketball round your answer to the nearest hundredth and show all your work and explain your answer
PLEASE HELP
Answer:
Viewing window: [0, 1.4] × [-3, 12]
See the attachments from the TI-83 Plus graphing calculator.
1) f(t) = -16t² + 15t + 6.5
2) -16t² + 15t + 6.5 = 0
32t² - 30t - 13 = 0
t = (30 + √((-30)² - 4(32)(-13)))/(2(32))
= (30 + √2564)/64
= (30 + 2√641)/64
= (15 + √641)/32
= about 1.26 seconds
3) f'(t) = -32t + 15
-32t + 15 = 0
t = 15/32 seconds = about .47 seconds
f(15/32) = -16(15/32)² + 15(15/32) + 6.5
= about 10.02 feet
Part 1: The function that models the height of the basketball is [tex]\( h(t) = -16t^2 + 15t + 6.5 \).[/tex]
Part 2: It takes approximately 0.89 seconds for the basketball to hit the ground.
Part 3: The basketball reaches its maximum height at approximately 0.47 seconds.
Part 1: The function that models the height of the basketball is given by:
[tex]\[ h(t) = -16t^2 + v_0 t + h_0 \][/tex]
Given:
- Initial velocity [tex](\( v_0 \))[/tex] = 15 ft/sec
- Initial height [tex](\( h_0 \))[/tex] = 6.5 feet
So, the function becomes:
[tex]\[ h(t) = -16t^2 + 15t + 6.5 \][/tex]
Part 2: To find how long it takes for the basketball to hit the ground, we set [tex]\( h(t) = 0 \)[/tex] and solve for [tex]\( t \)[/tex]:
[tex]\[ -16t^2 + 15t + 6.5 = 0 \][/tex]
We can use the quadratic formula to solve for[tex]\( t \)[/tex]:
[tex]\[ t = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \][/tex]
where [tex]\( a = -16 \), \( b = 15 \), and \( c = 6.5 \).[/tex]
Plugging in the values:
[tex]\[ t = \frac{-15 \pm \sqrt{15^2 - 4(-16)(6.5)}}{2(-16)} \]\[ t = \frac{-15 \pm \sqrt{225 + 416}}{-32} \]\[ t = \frac{-15 \pm \sqrt{641}}{-32} \][/tex]
Using a calculator, we find:
[tex]\[ t \approx 0.89 \text{ seconds (rounded to the nearest hundredth)} \][/tex]
Part 3: To find when the basketball reaches its maximum height, we can use the formula for the x-coordinate of the vertex of a quadratic function:
[tex]\[ t_{\text{max}} = -\frac{b}{2a} \][/tex]
For our function [tex]\( h(t) = -16t^2 + 15t + 6.5 \), \( a = -16 \) and \( b = 15 \).[/tex]
[tex]\[ t_{\text{max}} = -\frac{15}{2(-16)} \]\[ t_{\text{max}} = \frac{15}{32} \]\[ t_{\text{max}} \approx 0.47 \text{ seconds (rounded to the nearest hundredth)} \][/tex]
Part 4: To find the maximum height of the basketball, we substitute the value of [tex]\( t_{\text{max}} \)[/tex] into the function [tex]\( h(t) \):[/tex]
[tex]\[ h_{\text{max}} = -16(0.47)^2 + 15(0.47) + 6.5 \]\[ h_{\text{max}} = -16(0.2209) + 7.05 + 6.5 \]\[ h_{\text{max}} = -3.5344 + 7.05 + 6.5 \]\[ h_{\text{max}} \approx 10.0156 \text{ feet (rounded to the nearest hundredth)} \][/tex]
The maximum height of the basketball is approximately 10.02 feet.
Three more than the quotient of a number and 5 is equal to 9
Answer:
The number is 30.
Step-by-step explanation:
x/5+3=9
x/5=9-3
x/5=6
x=6*5
x=30
The number is 30.
Explanation:The given question is a mathematical equation.
Let's define the number as 'x'. According to the given equation, the quotient of the number and 5, which is x/5, when three is added to it, should be equal to 9. Mathematically, we can write this as:
x/5 + 3 = 9
To solve for x, we need to isolate x on one side of the equation. We can do this by subtracting 3 from both sides of the equation:
x/5 = 9 - 3
x/5 = 6
To get rid of the fraction, we can multiply both sides of the equation by 5:
x = 6 * 5
x = 30
Therefore, the number is 30.
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I need some help with this equation please!
Answer:
y = - 2x + 8
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = [tex]\frac{1}{2}[/tex] x - 9 ← is in slope- intercept form
with slope m = [tex]\frac{1}{2}[/tex]
Given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{1}{2} }[/tex] = - 2, thus
y = - 2x + c ← is the partial equation
To find c substitute (3, 2) into the partial equation
2 = - 6 + c ⇒ c = 2 + 6 = 8
y = - 2x + 8 ← equation of perpendicular line
can someone explain to me HOW to solve these problems
(2m)^3(m^4)^5
(-3y^5)^32y^2
plzzzz help
Answer:
(2m)^3(m^4)^5= 8m^23
(-3y^5)^3x2y^2= -54y^17
Step-by-step explanation:
1. For solving first part
(2m)^3(m^4)^5
=[tex](2^3 m^3) (m^{20} )\\Acoording \,to\,exponential\,rules \, exponent 4 \, and\, 5 \,were\, \,multiplied\\As\\\2^3 =8 \\so\\8m^3 \times m^{20} \\\\Acoording \,to\,exponential\,rules \, exponent \,3 \,and\,20\,will\,be\,added\\x^{2} 8m^{23}[/tex]
(2m)^3(m^4)^5= 8m^23
2. For solving second part
(-3y^5)^3 x 2y^2
[tex](-3^3) y^{5\times3} \times 2y^2\\\\As \,3^3= 27 \,and\\\\applying \,exponential\, rule \,the\, exponents\ 5 \, and\, 3 \,will\,be\,multiplied\\the \,equation will become\\-27 \,y15 \times 2y^2\\\\applying \,exponential\, rule \,the\, exponents\, 15 \,and\, 2 \,wil, be\,added \\-54 y^{17}[/tex]
(-3y^5)^3 x 2y^2= -54y^17
Keywords: Algebra
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Use the table to determine the average rate of change from 3 to 6 storms
The average rate of change in gas prices from 3 to 6 predicted storms is 0.04, indicating a consistent increase of $0.04 in gas price for each additional storm predicted during that period. (option A)
The average rate of change is calculated by finding the difference in gas prices divided by the difference in the number of predicted storms.
[tex]\[ \text{Average Rate of Change} = \frac{\text{Change in Gas Price}}{\text{Change in Number of Storms}} \][/tex]
For the given data:
- Change in Gas Price from 3 to 6 storms: 2.56 - 2.44 = 0.12
- Change in Number of Storms: 6 - 3 = 3
[tex]\[ \text{Average Rate of Change} = \frac{0.12}{3} = 0.04 \][/tex]
Therefore, the correct answer is 0.04. (option A)
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The complete question is:
The price of gas has been increasing over the last month. Renee believes there is a positive correlation between the number of predicted storms and the price of gas.
Number of Storms Predicted 1 3 4 6 7
Gas Price $2.34 $2.44 $2.49 $2.56 $2.61
Use the table to determine the average rate of change from 3 to 6 storms.
a. 0.04
b. 3
c. 0.12
d. 0.27
A baseball diamond is a square with corners at home plate, first base, second base, and third base. The distance between home plate and first base is 30 yards. What is the area of a baseball diamond?
A.
900 square yards
B.
120 square yards
C.
90 square yards
Answer:
A: 900 yards
Step-by-step explanation:
im sure... i had the same test question and got it right! pls give me brainliest
Answer:
900 sq. yd.
Step-by-step explanation:
So, we know that the baseball diamond is a square, so we use the equation of a square, A = [tex]a^{2}[/tex]
Since all sides of a square are equal, each is always gonna be 30 yards. So we substitute a for 30
A = [tex]a^{2}[/tex]
A = [tex]30^{2}[/tex]
A = 900 sq. yd.
Which gives you the area of the diamond as 900 sq. yd.
An object’s speed decreases by 6% for each minute that it is slowing down. What is the percent that it’s speed will decrease over half an hour?
to factory plants are making TV panels. Yesterday plant a produce 8000 panels 1% of the panels from plant a 4% of the panels from plant be where defective how many panels did plant be produced if the overall percentage of defective plants from the two plants was 2%
Answer:
[tex]Plant\ B\ produces\ 4000\ panels.[/tex]
Step-by-step explanation:
Let plant B produces [tex]x[/tex] panels.
Defective Panels from Plant A and Plant B
Defective panels from plant A[tex]=1\%\ of\ 8000[/tex]
Defective panels from plant A[tex]=0.01\times 8000[/tex]
Defective panels from plant A[tex]=80[/tex]
Defective panels from plant B[tex]=4\%\ of\ x[/tex]
Defective panels from plant B[tex]=0.04x[/tex]
Total Defective panels=Defective panels from plant A+Defective panels from plant B
Total Defective panels[tex]=80+0.04x[/tex]
Total Panels and defective panels:
Total Panels=Panels from plant A+Panels from plant B
Total Panels=8000+x
Total Defective panels[tex]=2\%\ of\ total\ panels=2\%\ of\ (8000+x)[/tex]
Total Defective Panels[tex]0.02\times (8000+x)=160+0.02x[/tex]
[tex]80+0.04x=160+0.02x\\\\0.04x-0.02x=160-80\\\\0.02x=80\\\\x=\frac{80}{0.02}\\\\x=4000[/tex]
A new car is purchasd for 20,300 dollars. The value of the car depreciates at 9.5% per year. What will be the value of the car be, to the nearest cent, after 11 years?
[tex]\bf \qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &20300\\ r=rate\to 9.5\%\to \frac{9.5}{100}\dotfill &0.095\\ t=\textit{elapsed time}\dotfill &11\\ \end{cases} \\\\\\ A=20300(1-0.095)^{11}\implies A=20300(0.905)^{11}\implies \stackrel{\textit{rounded up}}{A=6770.65}[/tex]
Answer:
$6770.65
this is rounded up
Step-by-step explanation:
Two angles are complementary three times the measure of one of the angles is 10° more than the measure of the other angle. find the difference between the measure of the larger angle in the smaller angle
Answer:
The difference is 40,
Step-by-step explanation:
Complementary angles , x+y =90
so we know angle 1, we call it 3x and angle 2 we call it y= 3x+10
so 3x +10= 90-x
4x=100
x=25
angle 1= 3(25) - 10
y= 65
65-25= 40
Answer:
40°
Step-by-step explanation:
Let x represent one of the angles, and y represent the other one. Then we have ...
x + y = 90
3x = y +10
Substituting for y in the first equation, we have ...
x + (3x -10) = 90
4x = 100
x = 25
y = 3(25) -10 = 65
The difference between the angles is ...
y -x = 65 -25 = 40 . . . . degrees
The difference between the angle measures is 40 degrees.
Vicky has baseball practice every 10 days . She starts on May 5 . Will she have practice on May 19? Yes or no and How do you know ?
Answer:no
Step-by-step explanation:
It'll be may 15th
if She starts on May 5 then there is no practice on May 19.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given that Vicky has baseball practice every 10 days
She starts on May 5 .
We have to find whether she has to practice on May 19.
From May 5 the ten days ends at may 15.
So on May 19 the practice is not there.
So no, Vicky does not practice on May 19.
Hence, if She starts on May 5 then there is no practice on May 19.
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Need some help with some questions:
1) What is the simplified form of:
[tex] \sqrt{8} + 5 \sqrt{2} [/tex]
2) Which fraction is equal to:
[tex] \frac{ \sqrt{3} + \sqrt{5} }{ \sqrt{3} } [/tex]
A.
[tex]3 + \sqrt{5} [/tex]
B.
[tex] \frac{2 \sqrt{3} + \sqrt{5} }{ \sqrt{3} } [/tex]
C.
[tex] \frac{3 + \sqrt{15} }{3} [/tex]
D.
[tex] \frac{3 + \sqrt{5} }{3} [/tex]
3) How many solutions are there for x if
[tex]y = {x}^{2} - 2 \: and \: 2x + y + 6 = 0[/tex]
4) Which equation has no simultaneous solution with:
[tex]y = {x}^{2} + 4[/tex]
A.
[tex]x = - 3[/tex]
B.
[tex]y = x + 4[/tex]
C.
[tex]y = 3x + 2[/tex]
D.
[tex]y = 2 - x {}^{2} [/tex]
5) Which one of these expressions is not rational?
A.
[tex]2 \sqrt{3} \times \sqrt{27} [/tex]
B.
[tex] \frac{2}{ \sqrt{8} } \times \sqrt{18} [/tex]
C.
[tex] \frac{3 \sqrt{42} }{ \sqrt{3} } [/tex]
D.
[tex] \sqrt{ \frac{4}{9} } [/tex]
Answer:
Question 1) 7 root 2
Question 2 ) c
Question 3) ?
Question 4) A
Question ) D
Answer:
1) 7 Root 2
2) C
3) 4
4) A
5) D
Step-by-step explanation:
Ashton makes more than 32 sandwiches for a party. If Ashton cuts each sandwich into two pieces, which inequality represents the total number of pieces, p, he has?
A. p < 64
B. p > 32
C. p < 32
D. p > 64
The inequality p > 64 represents the total number of pieces he has ⇒ D
Step-by-step explanation:
Let us revise the inequality words
Less than ⇒ <More than ⇒ >At least ⇒ ≥At most ⇒ ≤∵ Ashton makes more than 32 sandwiches for a party
∴ The number of sandwiches > 32
∵ Ashton cuts each sandwich into two pieces
- That the number of pieces is the number of sandwiches times 2
∴ The number of pieces > 2 × 32
∴ The number of pieces > 64
- The number of pieces is p
∴ p > 64
The inequality p > 64 represents the total number of pieces he has
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Select the smallest fraction from the following list of fractions. 2/3, 3/4, 1 1/2, 3/5, 2 2/3, 7/8
Answer:
The answer is 3/5
Step-by-step explanation:
Let's convert to decimals these fractions and mixed numbers to make the comparison and find out the smallest fraction, this way:
2/3 = 0.67
3/4 = 0.75
1 1/2 = 1 + 1/2 = 1.5
3/5 = 0.6
2 2/3 = 2 + 2/3 = 2.67
7/8 = 0.875
Now we observe that the lowest value is 0.6, therefore, the smallest fraction is:
3/5
To find the smallest fraction, compare and convert the fractions to have a common denominator. The smallest fraction from the given list is 7/12.
Explanation:To find the smallest fraction from the given list, we need to compare the fractions. One way to compare fractions is to make their denominators equal. Let's convert all the fractions to have a denominator of 12:
2/3 = 8/123/4 = 9/121 1/2 = 18/123/5 = 7/122 2/3 = 20/127/8 = 10.5/12From the conversions, we can see that the smallest fraction is 7/12.
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The graph shows the relationship between the hours a soccer team practiced after the season started and their total practice time for the year. a. How many hours did the soccer team practice before the season began?
Answer:
6 hours
Step-by-step explanation:
The picture of the question in the attached figure
Let
x ----> the hours a soccer team practiced after the season started
y ----> the total practice time for the year in hours
we know that
The y-intercept of a linear equation is the value of x when the value of y is equal to zero
In the context of this problem, the y-intercept is the total practice time before the season began (the value of x is equal to zero)
Looking at the graph
The y-intercept is the point (0,6)
therefore
the total practice time before the season began is 6 hours
Answer:
can yu show the picture?
Step-by-step explanation:
The height of a triangle is 5 m less than it’s base. The area of the triangle is 42 m^2 what is the length of the base
Answer:
12 meters
Step-by-step explanation:
Let b = base
then
b-5 = altitude
since we know that the area for any triangle is
(1/2)bh
where
b is base
h is height or altitude
(1/2)b(b-5) = 42
b(b-5) = 84
b^2-5b = 84
b^2-5b-84 = 0
(b-12)(b+7) = 0
b = {12, -7}
toss out the negative solution leaving:
b = 12 meters
Here is the set up:
A = (bh)/2
42 = [b • (b - 5)]/2
This is all you need. Solve the equation for b to find your answer.
The interest obtained after 1 year on an investment at 1 1/2% simple interest per year; x = number of dollars invested
Answer:
I = 0.015x
Step-by-step explanation:
To calculate the interest obtained from your investment after one year, multiply the interest rate by the investment.
You can use the formula I = Prt; where:
"I" is interest (Capital i).
"P" is principal, starting money or investment.
"r" is the interest rate converted to decimal form.
"t" is the time, usually in years.
Convert 1 1/2% to decimal form. First, change the mixed fraction percentage to a decimal percentage. Convert the percentage to decimal form by dividing by 100. This value will be "r". (Don't confuse decimal form with decimal form as a percentage).
1 1/2% = 1.5%
1.5% ÷ 100 = 0.015
r = 0.015
From the problem, we know the time is 1 year; t = 1.
We don't know the value for the principal, "P", but we are told to use the variable "x"; P = x
Using the bolded information, substitute them for the variables into the formula.
I = Prt
I = (x)(0.015)(1) Remember any number multiplied by "1" is not changed.
I = (x)(0.015) Change the standard formatting without brackets.
I = 0.015x Formula for the interest obtained after 1 year.
Interest obtained after 1 year in dollar is 0.015x
Given that;
Number of year = 1
Number of dollars invested = x
Rate of interest = [tex]1\frac{1}{2}[/tex]%
Find:
Interest obtained after 1 year
Computation:
Rate of interest = [tex]1\frac{1}{2}[/tex]% = 3/2 % = 1.5% = 0.015
Interest = (P)(R)(T)
Interest obtained after 1 year = (x)(1)(0.015)
Interest obtained after 1 year = 0.015x
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You are in charge of buying hamburgers and chicken for a party. The hamburgers cost $2 per pound and the chicken costs $3 per pound. You have $60 to spend. Write and solve a linear equation to find how much chicken you can afford to buy if you buy 12
pounds of hamburgers.
Linear equation is 2x + 3y = 60
Chicken that can be afforded is 48 pounds.
Step-by-step explanation:
Step 1:
Given details are cost of hamburgers per pound = $2 and cost of chicken per pound = $3, total amount for spending = $60
Step 2:
Form equation from given data.
Let x be number of hamburgers bought and y be number of chicken that can be bought.
⇒ 2x + 3y = 60
Step 3:
Given that 12 pounds of hamburgers can be bought. Then 2x = 12. Substitute in equation to find pounds of chicken
⇒ 12 + 3y = 60
⇒ 3y = 60 - 12 = 48
⇒ 3y = 48 pounds or y = 16 (number of chicken that can be bought)
Round the weight of the sweet potato chips to the nearest tenth of an ounce. 3.705
Answer:
Step-by-step explanation:
3.705 rounded to the nearest tenth of an oz = 3.7 <==
The weight of the sweet potato chips, when rounded to the nearest tenth, is 3.7 ounces.
Explanation:To round the weight of the sweet potato chips to the nearest tenth of an ounce, we look at the number in the hundredths place.
Since the weight is 3.705, and the number in the hundredths place is 0.005, we apply a basic rounding rule: if the number in the hundredths place is 5 or more, we round up the number in the tenths place.
Here, that means we round up '7' to '8'. Thus, when rounded to the nearest tenth of an ounce, the weight of the sweet potato chips is 3.7 ounces.
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steps of solving linear equations
5×10 to the ninth power
Answer:
5,000,000,000 or 1,953,125,000,000,000
Depends on what you mean
Step-by-step explanation:
If (5*10)^9
(50)^9
1,953,125,000,000,000
Or if 5 * (10)^9
5 * 1,000,000,000 = 5,000,000,000
Answer:1953125 x 10^9
Step-by-step explanation: 5^9= 1953125 and 10^9.
8v+1=7v-26 find the v
Answer:
V=-27
Step-by-step explanation:
8v+1=7v-26
-7v -7v
v+1=-26
-1 -1
v=-27
in the ordinary dating of invoices,what does n/ 45 means
Answer:
the net amount is due in 45 days
Step-by-step explanation:
Invoice terms often have a discount for early payment, and a specification as to the date by which payment in full is expected. n/45 means the net amount of the invoice is due in 45 days.
25) The angle measurements of triangle XYZ are shown in the
diagram below.
What kind of triangle is XYZ?
A) Acute
B) Obtuse
C) Right
D) Equiangular
Answer:
Right
Step-by-step explanation:
Triangle having ninety degree angle in it is right angle triangle.
Find the volume of a cube where the length of each side is 6 centimeters.
Answer:
V = 6³ = 216 cm³
The volume of this cube is 216 cm³.
The correct answer is [tex]\( \boxed{216 \text{ cm}^3} \).[/tex]
The volume of a cube is calculated by raising the length of one side to the power of three, or in other words, by multiplying the length of one side by itself three times. Given that the length of each side of the cube is 6 centimeters, the volume [tex]\( V \)[/tex] can be calculated as follows:
[tex]\[ V = a^3 \][/tex]
where [tex]\( a \)[/tex] is the length of a side of the cube. Substituting the given value:
[tex]\[ V = 6^3 \][/tex]
[tex]\[ V = 6 \times 6 \times 6 \][/tex]
[tex]\[ V = 216 \][/tex]
Therefore, the volume of the cube is [tex]\( 216 \)[/tex] cubic centimeters.
[tex]\( \boxed{216 \text{ cm}^3} \).[/tex]
There is a mountain with 30 bat caves in a row that contain 340 bats in all. Any 7 caves in a row contain exactly 77 bats. Suppose the first cave has 7 times more bats than the last caves. How many bats in the 29th cave?
Answer:
The 29th cave has 28 bats.
Step-by-step explanation:
It is given that any 7 caves in a row contain 77 bats.
So, out of the 30 caves, let us start counting from the second cave till the 29th cave(counting 28 caves).
7 times 4 gives us 28, which has [tex]77\times4=308[/tex] bats. We have not counted the first and last cave.
Let the number of bats in the last cave be [tex]x[/tex], then according to the question:
[tex]7x+x=340-308=32[/tex](First cave has 7 times more bats than the last cave)
Hence, [tex]x=4[/tex](number of bats in the 30th cave)
Now we shall again count, but this time from the first cave, leaving out the last 2 caves. So the total number of bats in the first 28 caves is 308 and 32 in the last 2 caves.
So, the number of bats in the 29th cave = 32 - 4 = 28