1. A number is as much greater than 21 as it is less than 71. Find the number
Solution -
Let the number be x.
x - 21 (number is as much greater than 21)71 - x (it is less than 71)As both the value of x - 21 and 71 - x is same hence,
=> x - 21 = 71 - x
=> x + x = 71 + 21
=> 2x = 92
=> x = 92/2
=> x = 46
Hence, the number is 46.
2. Find 2 consecutive natural number whose sum is 63.
Let the two consecutive numbers be x and x + 1.
=> x + (x + 1) = 63 (A.T.Q)
=> x + x + 1 = 63
=> 2x = 63 - 1
=> 2x = 62
=> x =62/2
=> x = 31
Hence, the consecutive natural numbers whose sum is 63 are 31 and 32.
Use synthetic division to find the expression for the area of the base of a rectangular prism with height x + 4 and volume x3 + 2x2 – 17x – 36.
2x2 – 9x
x2 + 6x – 24
x2 – 2x – 9
–4x2 + 8x + 36
The expression for the area of the base is x² – 2x – 9. Therefore, the correct answer is (C) x² – 2x – 9.
To use synthetic division, we first need to set up the divisor in the correct form. Since we are looking for the expression for the area of the base of the rectangular prism, we know that the volume of the prism is given by:
volume = (area of base) × (height)
We are given that the height is x + 4, and the volume is x³ + 2x² – 17x – 36. Therefore, we can write:
x³ + 2x² – 17x – 36 = (area of base) × (x + 4)
Now we can use synthetic division to find the expression for the area of the base. The divisor is x + 4, so we write:
-4 | 1 2 -17 -36
| -4 8 36
|-----------------
1 -2 -9 0
The last number in the bottom row is 0, which means that x + 4 is a factor of the polynomial. The other numbers in the bottom row give us the coefficients of the quotient polynomial. Therefore, we can write:
x³ + 2x² – 17x – 36 = (x + 4)(x² – 2x – 9)
So the expression for the area of the base is x² – 2x – 9. Therefore, the correct answer is (C) x² – 2x – 9.
Learn more about synthetic division here:
https://brainly.com/question/28824872
#SPJ7
The diameter of a circle is 28 millimeters. What is the circle's area
Use 3.14 for .
Answer:
615.44 mm²
Step-by-step explanation:
Before finding the area of the circle, first, let us find the radius of the circle.
Given that,
diameter ⇒ 28 mm
Therefore,
d = 2r28 = 2r
Divide both sides by 2.
14mm = radius
And now, let us find the area.
The formula to find the area of the circle is :
Area = π r²Let us solve now.
Area = π r²
= 3.14 × 14 × 14
= 43.96 × 14
= 615.44 mm²
D and E are the mid-points of the sides AB and AC of ΔABC and O is any point
on side BC. O is joined to A. If P and Q are the mid-points of OB and OC
respectively, then prove that DEQP is a parallelogram.
Check out the diagram below.
Since D and E are midpoints of AB and AC this means midsegment DE is parallel to side BC. Furthermore, it means DE is parallel to PQ because PQ is entirely on BC.
---------
Note how I drew a line from A to O. This forms two triangles ABO and ACO
For triangle ABO, segment DP is a midsegment because D and P are midpoints of AB and OB respectively. This means side DP is parallel to side AO. Keep this in mind as we'll use it later.
For triangle ACO, segment EQ is parallel to AO because EQ is a midsegment for similar reasons as already mentioned (E and Q are midpoints of AC and OC respectively). So this must mean that AO is parallel to EQ
Now chain the arguments together: if DP || AO and AO || EQ, then DP || EQ by the transitive property.
-----------
In short, we've proven two things
DE is parallel to PQDP is parallel to EQThis is enough to conclude that DEQP is a parallelogram. By definition, a parallelogram has two pairs of opposite parallel sides.
Answer:
Points
Step-by-step explanation:
find the first six terms of the geometric sequence-1, -3, -9, _, _, _
Hey there!
A geometric sequence is where we use multiplication or division to get to the next term.
In this case, we use multiplication (we multiply every term by 3)
So we have
-1, -3, -9, -27, -81, -243...
Steps:
Since we multiply every term by 3, we multiply -9 times 3. then we multiply the product of 9 & 3 times 3, and so on...Hope everything is clear.
Let me know if you have any questions; if oyu do, kindly comment below my answer.
#LearningDoesn'tEnd
[tex]\rule{200}{2}[/tex]
Altogether a torch and battery cost £2. 50
torch costs £2 more than battery how much does battery cost in the simplest for fraction
3(x+5)+10
Please help
Answer:
3x+15+10
3x + 25
Step-by-step explanation:
Answer:
3x + 25
Step-by-step explanation:
3
Justine and her friends went out for dinner Friday
night. The bill came to $76.96. If they split the bill
evenly and each person paid $19.24, how many
friends, including Justine, were at dinner?
Answer:
A total of four people
Step-by-step explanation:
Answer:
4
Step-by-step explanation
divide 19.24 from 76.96.
and that gives you how many friends
What is the cost, in dollars, for 1 box of pasta
Answer:
.99 cents. i think but for a pAck two dollars
Step-by-step explanation:
internet
Answer:
.99 cents. i think but for a pack two dollars
Step-by-step explanation:
Write an equation that represents the line.
Use exact numbers.
Answer:
3x - 4y + 8 = 0
Step-by-step explanation:
In figure,
When x = 0, y = 2
x = 4, y = 5
Two points on the line are (0, 2) & (4,5).
Slope = (5 - 2)/(4 - 0)= 3/4
Equation is:
=> y - 2 = (3/4)(x - 0)
=> y - 2 = 3x/4
=> 4y - 8 = 3x
=> 3x - 4y + 8 = 0
The graph below shows a company's profit f(x), in dollars, depending on the price of goods x, in dollars, being sold by the
company:
f(x)
150
120 +
90
60
30
х
2
3
4
5
7
-
-3 -2 -1
-30
8
11
Part A: What do the x-intercepts and maximum value of the graph represent in context of the described situation?
Part B: What are the intervals where the function is increasing and decreasing, and what do they represent about the sale and
profit for the company in the situation described?
Part C: What is an approximate average rate of change of the graph from x = 1 to x = 3, and what does this rate represent in
context of the described situation?
a = −b
b = −c
a + b + c = 8
Answer:
8
Step-by-step explanation:
if a = -b, then -a = b.
plug that into the (b = -c) problem, and you get -a = -c, or a = c
if a and c ar equal, then and b = -c, b also equals -a.
the problem then becomes a - b +c, where a = 8, c = 8, and b = -8
a = -b -> 8 = -(-8)
b = -c -> -8 = -(8)
a = c -> 8 = 8
Estimate the percent of apartment residents who pay less than $700 per month.
A. 60%
B. 75%
C. 50%
D. 55%
According to the graph, it is found that the percent of apartment residents who pay less than $700 per month is given by:
B. 75%
What does the graph states?It states that:
Around 5% of the respondents pay less than $600 in rent.25% pay between $600 and $649.45% pay between $650 and $699.25% pay between $700 and $749.5% of the respondents pay more than $749 in rent.Hence, for less than $700, we have that:
5% + 25% + 45% = 75%.
Thus option B is correct.
More can be learned about percentages at https://brainly.com/question/10491646
how many inches are in 10 yards? Please show all work and if i have to divide or multiply.
Answer:
1 yard is 3 feet. There is 36 inches in a yard. There is 12 inches in a foot. Multiply 36 by 10 to get 360. There is 360 inches in 10 yards.
Step-by-step explanation:
Hope this helps! :)
have a blessed day and remember to keep smiling! :)
PLEASE MARK ME AS BRAINLIEST I REALLY WANT TO LEVEL UP
A father is 34 years of age. At present his son is 8 years old. In how many years will the father be three times as old as his son ? (11 6 years (3) 4 years (2) 5 years (4) 3 years
Christopher plays quarterback for a
neighborhood football team. During
his team's first game, he executed
60 plays, 42 of which were successful.
What percent of Christopher's plays
were successful?
Answer:
70%
Step-by-step explanation:
[tex]42\div60[/tex]
Calculate
[tex]\frac{42}{60}[/tex]
Cross out the common factor
[tex]\frac{7}{10}[/tex]
Multiply a number to both the numerator and the denominator
[tex]\frac{7}{10}\times\frac{10}{10}[/tex]
Write as a single fraction
[tex]\frac{7\times10}{10\times10}[/tex]
Calculate the product or quotient
[tex]\frac{70}{10\times10}[/tex]
Calculate the product or quotient
[tex]\frac{70}{100}[/tex]
Rewrite a fraction with denominator equals 100 to a percentage
[tex]70[/tex]%
I hope this helps you
:)
I need help on number 4 please help!*Will mark Brainlest*
Answer:
i guess 3 rd option is correct. ........hope it helps u ♥♥♥♥
Write the equation of the line that passes through the given point and has the given slope. (-12,5)
slope = 1/3
Answer: y= 1/3x + 41
Answer:
[tex]_{\text{point-slope form}}[/tex]
[tex]\huge\boxed{y-5=\dfrac{1}{3}(x+12)}[/tex]
[tex]_{\text{slope-intercept form}}[/tex]
[tex]\huge\boxed{y=\dfrac{1}{3}x+9}[/tex]
[tex]_{\text{standard form}}[/tex]
[tex]\huge\boxed{x-3y=-27}[/tex]
Step-by-step explanation:
The point-slope form of an equation of a line:
[tex]y-y_1=m(x-x_1)[/tex]
where
[tex]m[/tex] - slope
[tex](x_1;\ y_1)[/tex] - a point on a line
We have
[tex]m=\dfrac{1}{3};\ (-12;\ 5)\to x_1=-12;\ y_1=5[/tex]
Substitute:
[tex]y-5=\dfrac{1}{3}(x-(-12))\\\\y-5=\dfrac{1}{3}(x+12)\\==================[/tex]
[tex]y-5=\dfrac{1}{3}(x+12)\qquad|\text{use the distributive property}\ a(b+c)=ab+ac\\\\y-5=\dfrac{1}{3}x+4\qquad|\text{add 5 to both sides}\\\\y=\dfrac{1}{3}x+9\\=======================[/tex]
[tex]y=\dfrac{1}{3}x+9\qquad|\text{multiply both sides by 3}\\\\3y=x+27\qquad|\text{subtract}\ x\ \text{from both sides}\\\\-x+3y=27\qquad|\text{change the signs}\\\\x-3y=-27[/tex]
Write an equation of a line that passes through the point Z (6, – 2) and is perpendicular to the line y=-1/3x + 2
Answer:
y = 3x - 20
Step-by-step explanation:
First, we have to find the slope of the equation. We can do by taking the opposite reciprocal of the slope of the original line.
The opposite reciprocal of-1/3 is 3/1 or 3.
So, the slope of our equation will be 3. Our equation so far is:
y = 3x + b.
To find b, or the y-intercept of the line, we can simply substitute the given coordinates into the equation. If we replace x with 6 and y with -2 and solve the equation, we can find the value of b.
-2 = 3(6) + b
-2 = 18 + b
-2 - 18 = b
b = -20
So the equation is,
y = 3x -20.
To check our equation, we can again substitute the coordinates into the equation and solve. If both sides are equal, then the equation is correct.
-2 = 6(3) - 20
-2 = 18 - 20
-2 = -2
The two lines are perpendicular if a 90° angle is formed when they
intersect.
The equation of the line that passes through point Z(6, -2) and is perpendicular to the line [tex]y = -\dfrac{1}{3} \cdot x + 2[/tex] is ; y = 3·x - 20
Reason:
The equation of the required line is, y = 3·x - 20
The given point is Z(6, -2)
Perpendicular to the line, [tex]y = -\dfrac{1}{3} \cdot x + 2[/tex]
Solution:
The slope of a line perpendicular to another line having a slope, m, is [tex]-\dfrac{1}{m}[/tex]
The slope of the given line is [tex]-\dfrac{1}{3}[/tex]
The slope of the perpendicular line is therefore;
[tex]m = -\dfrac{1}{\left(-\dfrac{1}{3}\right)} = \dfrac{3}{1} = 3[/tex]
The point and slope form of the equation of the given line is therefore;
y - (-2) = 3·(x - 6)
y + 2 = 3·x - 3×6 = 3·x - 18
y = 3·x - 18 - 2 = 3·x - 20
y = 3·x - 20
The equation of the line that passes through point Z(6, -2) and is perpendicular to the line [tex]y = -\dfrac{1}{3} \cdot x + 2[/tex] is therefore;
y = 3·x - 20
Learn more here:
https://brainly.com/question/14105283
A merchant offers a large group of items at 32% off. Later, the merchant takes 16% off these sale prices and claims that the final price of these items is 186 off the original price. What is the total percent discount?
The total percent discount offered by the merchant is 57.12%.
What is the total percent discount?A discount is when the price of an items is reduced. It makes a good cheaper when a discount is applied.
The percent change in price after the first discount = 100% - 32% = 68%
The final price after the second discount = (100 - 16%) x 68%
= 57.12%
To learn more about how to calculate discounts, please check: https://brainly.com/question/26061308
I need ans for this.....please I will mark brainliest..
Answer:
(1,2), (2,4) (2.5,5) (3,6) (4,8) (5,10) (6,12) (15,30)
Step-by-step explanation:
2.5/2.5 = 1
5/2.5 = 2
(1,2), (2,4) (2.5,5) (3,6) (4,8) (5,10) (6,12) (15,30)
Have an amazing day!
PLEASE RATE!
Please Answers these
AND NO LINKS PLEASE
Answer:
10: 112.5
12: 84
13: T F T
14: F T T
15: T F T
Is 7 a solution to the compound inequality
Answer:
yes
Step-by-step explanation:
any number more than 5 works, even 5.01
Cranberry juice costs $6.30 per quart and apple juice costs $3.60 per quart. Terrence wants to know how many quarts q of cranberry juice he should mix with 4 quarts of apple juice to make cranberry-apple juice. He also wants to sell the juice at cost for $4.50 per quart. Which equation below represents the situation?
A. 3.60(q – 4) + 25.20 = 4.50q
B. 3.60q + 25.20 = 4.50(q + 4)
C. 6.30(q – 4) + 14.40 = 4.50q
D. 6.30q + 14.40 = 4.50(q + 4)
Answer:
The correct answer is D
Step-by-step explanation:
Cost of q quarts of Cranberry juice will be: $ 6.30q and cost of 4 quarts of apple juice will be $ (3.60×4)= $ 14.40. Total quarts of items would be q+4 , and he also wants to sell the juice at cost for $4.50 per quart. That means that the total cost to sell the juices will be $4.50(q+4) . Also, Total cost= Cost of q quarts of cranberry juice+cost of 4 quarts of apple juice.
Please help
45−3x=18x
Answer:
Your answer is: x = 15/7
Isolate the variable by dividing each side by factors that don't contain the variable.
Step-by-step explanation:
Hope this helped : )
Sue jarred 30 ounces
of jam in 3 days.
How many ounces
of jam can Sue jar
in 5 days?
It’s one of those 2.
Answer:
50 ounces
Step-by-step explanation:
hope it helps you
Follow on insta for more help ankitakki45
thanks
What should i pick?!!
Answer:125x^6y^6 (Red)
Step-by-step explanation: To find the answer we need to do first 5^3 which is 125. Then according to exponent rule, we multiply the exponents inside by the exponent outside, so it would be x^6 and y^6.
It would be 125x^6y^6.
Hope this helps you!
how do i do objective function
Answer:
Find the appropriate form for your objective function Then you will describe which solvers can handle complex then, you pass the extra Parameters finally, the function argument details.
Help. (26. Is the question number.)
Answer:
9x^5*y^2*pi
Step-by-step explanation:
a = pi * r^2
a = pi * 9x^5y^2
a = 9x^5y^2pi
Let me know if you have questions or need help
2:3 = %
2:3 is in ratio change to percentage
Answer:
2:3 = 66%
Step-by-step explanation:
⇒ Convert the fraction 2/3 into decimal
⇒ 2/3 = 0.666
⇒ Multiply the decimal by 100: 0.66 × 100 = 66%
Therefore, the solution is 66%.
tell whether the relationship is a proportional relationship ( explain why or why not)PLEASE, PLEASE HELP ME ANSWER IT RN IT IS DUE TODAY!!!