Answer:
(7x^2+3)( 3x+5)
Step-by-step explanation:
21x^3 + 35x^2 + 9x + 15.
We will do factor by grouping
Rearranging the terms so I have the terms with a factor of 3 first and 5 last
Factor a 3x from the first two terms and 5 from the last two terms
21x^3 + 9x + 35x^2+ 15
3x(7x^2 +3) +5(7x^2+3)
Now factor out a (7x^2+3)
(7x^2+3)( 3x+5)
Answer:
Cubic = (3x + 5)(7x^2 + 3)
Step-by-step explanation:
If you make up two groups of 2, you might be able to factor this using the distributive property. Let's try it.
First group: 21x^3 + 35x^2 Take out 7x^2 as a common fact
First group: 7x^2(3x + 5)
Second group: 9x + 15 The HCF is 3
Second group: 3(3x + 5)
Now put your factors together in one long string.
Cubic = group 1 + group 2
Cubic = 7x^2 (3x + 5) + 3(3x + 5)
Note: If you had something like 7x^2 * y + 3 *y then you should see that the factors are y* (7x^2 + 3). So to solve the cubic, you should observe that (3x + 5) is a common factor.
Let y = 3x + 5
y(7x^2 + 3) Now substitute back for the y.
Cubic = (3x + 5)(7x^2 + 3)
I Need Help!! Answer Please!!
Answer:
50 degrees
Step-by-step explanation:
all inside angles in every triangle can be added up to equal 180 degrees.
this is a right angle, so one has to be 90 degrees
on the bottom right it's marked 140 degrees on the outside, in order to find the inside angle, you need to subtract 140 from 180, which gives you 40 degrees
180-90=90
90-40=50
so the answer is 50
if that's not clear enough leave a comment, hope this helps!
Answer:
50°
Step-by-step explanation:
Inside angles of a triangle = 180°
The triangle shown is a right triangle.
Therefore, it is 90°
180 - 90 = 90
90 - 40 = 50
Answer = 50°
Hair color. |. Clothing
Brown. I Dress
Black. I Jumpsuit
Blonde. I Pajamas
Red. I Jeans
The table above shows hair colors and clothing available at a doll shop. How many different combinations of hair color ND clothing are there?
Answer:
16 possible hair/clothing combinations
Step-by-step explanation:
1) Brown-dress; 2)Brown-jumpsuit; 3)Brown-pajamas ; 4)Brown-Jeans; 5)Black-Dress; 6)black jumpsuit; 7)black pajamas; 8)black jeans; 9)blonde dress; 10)blond jumpsuit; 11)blonde pajamas; 12)blond jeans; 13)red dress; 14)red jumpsuit; 15)red pajamas; 16)red jeans
Or just multiply 4x4 because there were four of each.
What number :Increased by 130% is 69 ?
130% as a decimal is 1.3
Divide 69 by 1.3:
69 /1.3 = 53.076923
Round the answer as needed
To find the original number that increased by 130% equals 69, we divide 69 by 2.30, which reveals that the original number is 30.
The student is asking how to find a number that, when increased by 130%, results in 69. To solve this problem, let's represent the original number as x. The increase by 130% of the original number would be x + 1.30x (which equals 2.30x), and this sum is equal to 69. To find x, we divide 69 by 2.30:
x = 69 / 2.30
We calculate this as:
x = 30
Therefore, the number which when increased by 130% equals 69 is 30.
The average of a set of 5 numbers is 44. If the number 50 is added to the set, what is the new average?
Answer:
45
Step-by-step explanation:
Um, If we say that all the numbers are 44, and now we add 50, then we will get 270. Find the mean of 270. We get 45.
Final answer:
To find the new average after adding 50 to a set of 5 numbers with an average of 44, multiply the average by the number of elements, add the new number, then divide by the total number of elements to get the new average of 45.
Explanation:
The average of a set of 5 numbers is 44. To find the sum of the original set, multiply the average by the number of elements: 44 x 5 = 220. When 50 is added, there are now 6 numbers in the set. To find the new average, divide the new sum (220 + 50 = 270) by the total number of elements (6) to get 45 as the new average.
- (1-7x) -6 (-7-x) = 36
Solving for x:
Start by distributing the numbers outside the parentheses to inside the parentheses:
-1 + 7x + 42 + 6x = 36
Now combine like (similar) terms:
13x + 41 = 36
Subtract 41 from both sides:
13x = -5
Divide both sides by 13:
x = [tex]-\frac{5}{13}[/tex]
Therefore, x = [tex]-\frac{5}{13}[/tex].
Hope this helps! :)
Please answer, will mark brainliest :)
Daniel has $500 in his school lunch account at the beginning of the school year.
By the end of the year he needs at least $100 in the account to roll into the next school year. Each week during the school year, he spends $15 on lunches. Write an inequality that represents the amount of money that Daniel will have to have in his account.
Answer:
100>=500-15x
Step-by-step explanation:
He needs at least 100, so it's greater than OR equal to 100. He starts with 500 and goes down 15 each week. The x stands for the amount of weeks that are in the school year. Sorry for the terrible formatting on the greater than or equal to.
To write an inequality representing Daniel's lunch account scenario, where he begins with $500 and must have at least $100 by year-end despite spending $15 weekly, the inequality would be: 500 - 15x >= 100.
The question involves writing an inequality to represent the condition where Daniel must have at least $100 in his school lunch account by the end of the school year, given he starts with $500 and spends $15 each week on lunches. To frame the inequality, let's denote the number of weeks Daniel buys lunch as x. Given he spends $15 per week, the total expenditure over x weeks will be $15x. Initially having $500 and requiring at least $100 by the end of the school year, the inequality will be:
500 - 15x ≥ 100.
This inequality states that even after spending $15 each week for x weeks, Daniel must have at least $100 remaining in his account. To find how many weeks he can afford to buy lunch while meeting this requirement, one would solve for x in the inequality.
20 points!!!
If two lines are perpendicular to the same line are they perpendicular to each other?
Answer:
no
Step-by-step explanation:
Answer:
Step-by-step explanation:
depending on the space you're considering, it would be SOMETIMES true. But usually, the 2 lines would be parralel.
What i'm saying is, that in an euclidian space, the 2 lines would be parallel. In another kind of space, the two lines could be anything...
for example: look at how longitude and lattitude are represented on a globe : they are "lines"... 2 sets of perpendicular lines...
Now look at what happens in the poles : all lines intersect! (therefore, they're not parallel, and not necessarily perpendicular either)
The domain of r:(3,-2)(1,2)(-1,-4)(-1,2)
Answer:
domain {-1,1.3}
Step-by-step explanation:
The domain is the input values, or in this case the first or x values
domain {3,1,-1,-1}
We do not put the same value twice
domain {3,1,-1}
We like to put them in numerical order
domain {-1,1.3}
what is another way to write the function f(x) = 5^x. The choices are
f(x)=(625^x)1/125
f(x) = 1/125(625^x)
f(x) = (625^x)^1/4
f(x) = 1/4(6256x)
Answer:
Correct answer is f(x) = (625^x)^1/4
Step-by-step explanation:
We know that
625 = 5^4
This means
f(x) = (625^x)^1/4
f(x) = (5^(4x))^1/4
But we know this is equivalent to
f(x) = (5^(4x*(1/4))) =
= 5^(x)
Correct answer is f(x) = (625^x)^1/4
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar. The measurement of angle B is °. The measurement of angle A is °. The measurement of angle C is °.
Answer:
B = 135
A = 60
C = 75
Hope this helps
Answer:
∠B = 135°
∠A = 60°
∠C = 75°
Step-by-step explanation:
Since, Straight Line PQ always has angle 180°
∴ ∠PBS = 180 - ∠ABC
= 180° - 45° = 135° = ∠B
Since, ∠RAS and ∠BAC are vertically opposite to each other.
So, ∠RAS = ∠BAC
Also ∠RAS = 60°
∴ ∠BAC = 60° = ∠A
The straight line ∠PCQ always has angle 180°.
∴ ∠PCR = 180 - ∠RCQ
⇒ ∠PCR = 180 - 105° = 75° = ∠C
what are solutions to the quadratic equation 2x^2+6x-10=x^2+6
Answer:
x = -2 or x = 8Step-by-step explanation:
[tex]2x^2+6x-10=x^2+6\qquad\text{subtract}\ x^2\ \text{and 6 from both sides}\\\\x^2+6x-16=0\\\\x^2+2x-8x-16=0\\\\x(x+2)-8(x+2)=0\\\\(x+2)(x-8)=0\iff x+2=0\ \vee\ x-8=0\\\\x+2=0\qquad\text{subtract 2 from both sides}\\x=-2\\\\x-8=0\qquad\text{add 8 to both sides}\\x=8[/tex]
Answer:
2 and -8
Explanation is Apex
Max saved some money by buying a book of 10 movie passes rather than individual tickets.Howcan he figure out how much money he saved?
Which of the following values is a solution for the inequality statement? Select all that apply. 11 > a/4 -16 55 -150 210 -78 108
Answer:
55, -150, -78
Step-by-step explanation:
The given inequality is:
[tex]11>\frac{a}{4}-16[/tex]
Adding 16 to both sides, we get:
[tex]11+16>\frac{a}{4}-16+16\\\\ 27>\frac{a}{4}[/tex]
Multiplying both sides by 4, we get:
[tex]27 \times {4}>\frac{a}{4} \times 4\\\\ 108>a[/tex]
Hence, the solution to the inequality is 108 > a or this can be written as a < 108
This means, the values less than 108 are a solution of the given inequality. 108 is not a part of the solution as the inequality symbol says less than 108.
Among the given options following are the values that are less than 108 and thus will satisfy the inequality:
55, -150, -78
what is the inverse of the function f(x)=2x+1
Answer:The inverse of the linear function f(x)=2x+1 is f^(-1) (x) = (1/2)x-1/2
Step-by-step explanation:
LOOK AT PICTURE PLEASE ANSWER ASAP parabola directrix focus and vertex
Answer:
[tex]y = - \frac{3}{20} {x}^{2} [/tex]
Step-by-step explanation:
The given parabola has focus at:
[tex](0, - \frac{5}{3} )[/tex]
and directrix at
[tex]y = \frac{5}{3} [/tex]
This is a vertical parabola that opens downwards.
The equation is of the form;
[tex] {x}^{2} = - 4py[/tex]
p is the distance from the vertex to the directrix.
Since the vertex is at the origin, we have
[tex]p = \frac{5}{3} [/tex]
We plug this value into the equation to get:
[tex] {x}^{2} = - 4( \frac{5}{3} )y[/tex]
[tex] {x}^{2} = - \frac{20}{3} y[/tex]
We solve for y to obtain:
[tex]y = - \frac{3}{20} {x}^{2} [/tex]
The 3rd option is correct.
Find the range of the data sources: 83,77,88,93,97,79,94,80,97,81
Let r = range
Range = biggest value minus smallest value
r = 97 - 77
r = 20
Answer:
Range 20
Step-by-step explanation:
First put all the numbers in order from least to greatest
77,79,80,81,83,88,93,94,97,97
To find range you subtract the largest number from the smallest number.
So 97 - 77 = 20
The range is 20
Hope This Helps!! :}
If two angles of a triangle are congruent, then the sides opposite those
angles are congruent.
That's true: if a triangle has two congruent angles, then it's an isosceles triangle.
An isosceles triangle has two congruent sides, which are opposite to the congruent angles, and a base, which is the side opposite to the non-congruent angle.
What is the area of ABC? Helppppp
Answer:
6 square units (rounded to nearest whole number)
Step-by-step explanation:
Area of triangle is found by the formula 1/2 * base * height
But we can't easily figure this out using this formula, instead we use another formula for area of a triangle:
[tex]A=\frac{1}{2}abSinC[/tex]
Where
A is the area
a and b are the two side given (3 and 5 in our case)
C is the angle between a and b (53 degrees given)
We can substitute into the formula and figure out:
[tex]A=\frac{1}{2}abSinC\\A=\frac{1}{2}(3)(5)Sin53\\A=5.99[/tex]
The area is 5.99, to the nearest whole number, the area is 6
What is the vertex and the equation of the axis of symmetry of the graph of y=x^2-6x-7
for a vertically opening parabola, its axis of symmetry will come from the x-coordinate of its vertex, thus
[tex]\bf \textit{vertex of a vertical parabola, using coefficients} \\\\ y=\stackrel{\stackrel{a}{\downarrow }}{1}x^2\stackrel{\stackrel{b}{\downarrow }}{-6}x\stackrel{\stackrel{c}{\downarrow }}{-7} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left( -\cfrac{-6}{2(1)}~~,~~-7-\cfrac{(-6)^2}{4(1)} \right)\implies (3~~,~~-7-9)\implies (3~~,~~-16) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \stackrel{\textit{axis of symmetry}}{x=3}~\hfill[/tex]
A patient’s weight is recorded as 75 kilograms. How many pounds does the patient weigh?
Answer:
165.347 pounds ..
Step-by-step explanation:
The weight of patient is given in kilograms which is
W = 75 kilo grams.
In order to convert the weight into pounds we have to multiply or divide 75 with some number.
There are 2.20462 pounds approximately in one kilogram.
So the weight in pounds will be:
Weight in pounds = 75 * 2.20462
= 165.3465 pounds
= 165.347 pounds ..
A alone can complete a work in 16 days and B alone can complete the work in 12 days. How many days will it take to complete the work if they work on alternate days starting from A.
Answer:
14 days
Step-by-step explanation:
1. Convert the amount of work person A and B can do respectively in one day into fractions.
A = 1/16 B = 1/12
2. Get both fractions to a common denominator using the least common multiple. This is 48.
1/16 × 3 = 3/48 1/12 × 4 = 4/48
3. Add both fractions to find out how much work will be done in two days. We are doing this because we are working in a pattern, and this will allow us to multiply, which is more time efficient than repeatedly adding 3 and then 4.
3/48 + 4/48 = 7/48
4. Figure out how many sets of two days work (7/48) will get them to 48/48 (100% done) or closest to it without being under. This would be 7 sets.
7/48 × 7 = 49/48
5. Multiply 7 by 2. We are doing this because we worked in sets of two days to account for A working and then B, since they are taking turns.
7 × 2 = 14
6. It will take them 14 days.
Write an equation: 1/5 of a shipment of books weights 25 pounds
To find the total weight of the shipment where [tex]\frac{1}{5}[/tex] weighs 25 pounds, we use the equation [tex]\frac{1}{5}[/tex]W = 25 and solve for W, leading to a total weight of 125 pounds.
The question is asking us to write an equation that represents the situation where [tex]\frac{1}{5}[/tex] of a shipment of books weighs 25 pounds.
To find the total weight of the shipment, we should set this up as an equation where the total weight of the shipment is represented by W. Since [tex]\frac{1}{5}[/tex] of the shipment weighs 25 pounds, we can write the equation as [tex]\frac{1}{5}[/tex] W = 25.
To find the weight of the whole shipment, we need to multiply both sides of the equation by 5, which will give us
W = 125 pounds.
When converting units such as pounds to ounces, we use the unit equivalence 1 pound = 16 ounces.
If the weight of the books needed to be in ounces, we could convert 125 pounds by multiplying
125 x 16 = 2000 ounces
What is the slope of the line through (-7, -2) and (-6, 7)?
Make sure to explain your answers, please!
{No spam answers, please! Thank you!}
Answer:
[tex]\displaystyle =9[/tex]
Step-by-step explanation:
The slope formula is
[tex]\displaystyle \frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\displaystyle y_2=7\\\displaystyle y_1=(-2)\\\displaystyle x_2=(-6)\\\displaystyle x_1=(-7)[/tex]
[tex]\frac{7-(-2)}{(-6)-(-7)}=\frac{9}{1}=9[/tex]
Therefore, the slope is 9, and the correct answer is 9.
Hope this helps!
A 279-foot rope is cut into three pieces. The second piece is twice as long as the first. The third piece is as long as the second. How long is each piece of rope?
Step-by-step explanation:
Let's say x is the length of the first piece.
The second piece is 2x.
The third piece is 2x.
So the total length is:
x + 2x + 2x = 279
5x = 279
x = 55.8
That means 2x = 111.6.
So the first piece is 55.8 feet, the second piece is 111.6 feet, and the third piece is also 111.6 feet.
Answer:
Piece 1 : 55.8 ft
Piece 2: 111.6 ft
piece 3: 111.6 ft
Step-by-step explanation:
From the question we can see that the total length of the rope is 279 ft and as mentioned it is cut into three pieces. Since the first piece has no length we can give it a variable of x . Piece two is twice as long as piece one, so we can give it a value of 2x . Lastly, piece three is the same as piece two, so it would also be 2x.
So we can now say the following:
[tex]x + 2x + 2x = 279ft[/tex] .... now we can solve for x.
[tex]5x = 279[/tex]
[tex]x = 55.8 ft[/tex]
So we can see that piece one is 55.8 ft long . Now we can use this value to find pieces two and three.
[tex]2x = P2[/tex]
[tex]2(55.8) = P2[/tex]
[tex]111.6 = P2[/tex]
So pieces two and three are 111.6 ft long
I hope this answered your question. If you have any more questions feel free to ask away at Brainly.
True or false? If you took a true "if-then" statement, inserted a not in each clause, and reversed the clauses, the new statement would also be true.
Answer:
The correct answer would be true. Reversing the statement clause and inserting a "not" in a if- then statement will also make the new statement true. For example, "If I eat this, then give me five dollars". The reverse would be " If I do not eat this, then do not give me five dollars". Both sentences mean the same.
Step-by-step explanation:
Answer:
its true
Step-by-step explanation:
What are the factors of x^2 - 81
(X + 9)(x -9)
(x-9)(x -9)
(x + 3)(x - 27)
Prime
Answer:
A. x-9 and x+9 because these are perfect squares. 9 times -9 is -81. x times x is x^2. 9 + -9 is 0
Find the area of the rhombus. (4)
Answer:
24 cm2 is the answer or option d
Step-by-step explanation:
What is the median of this distribution?
Answer:
4
because if you cross off one number at a time from each side you are left with 2 number 4s and 4+4/2=4
Solve for x -2x + 5 <7
Answer:
[tex]\large\boxed{x>-1}[/tex]
Step-by-step explanation:
In this question, we're trying to solve for x.
In other words, we're going to need to get x by itself in order to get our answer for the inequality.
Solve:
[tex]-2x + 5 <7\\\\\text{Subtract 5 on both sides to get -2x by itself}\\\\-2x<2\\\\\text{Divide both sides by -2}\\\\\text{Since you're dividing by a negative, the} < \text{will flip to} >\\\\x>-1[/tex]
When you're done solving, you should get x > -1
This means that when you solve for x, you should get x > -1
I hope this helped you out.Good luck on your academics.Have a fantastic day!There are 32 more apple than oranges in a box. 3/5 of the oranges and 1/3 of the apples are overripe. If the number of overripe apples and the number of oranges is the same, how many pieces of overripe fruit are there?
The answer is:
There is a total of 48 overripe fruit.
Why?To calculate the number of pieces of overripe fruit we have, we need to write two equations to create a relationship between the number of apples and oranges.
Let be "x" the number of oranges, so:
[tex]Oranges=x\\Apples=x+32[/tex]
Now, we know that 3/5 of the oranges and 1/3 of the apples are overripe, so:
[tex]OverripeApples=\frac{1}{3}(x+32)\\\\OverripeOranges=\frac{3}{5}(x)[/tex]
Then, we have a condition that states that the number of overripe apples and overripe oranges is the same, so:
[tex]\frac{1}{3}(x+32)=\frac{3}{5}(x)[/tex]
[tex]\frac{1}{3}(x)+\frac{1}{3}(32)=\frac{3}{5}(x)[/tex]
[tex]\frac{1}{3}(32)=\frac{3}{5}(x)-\frac{1}{3}(x)[/tex]
[tex]\frac{1}{3}(32)=\frac{3x*3-1*x}{15}=\frac{9x-5*x}{15}=\frac{4x}{15}[/tex]
[tex]\frac{32}{3}=\frac{4x}{15}[/tex]
[tex]\frac{32*15}{3}=4x[/tex]
[tex]\frac{480}{3}=4x[/tex]
[tex]160=4x[/tex]
[tex]\frac{160}{4}=x[/tex]
[tex]40=x[/tex]
Therefore, we have that there are 40 oranges and 72 apples (40+32).
Now, calculating the number of overripe oranges and apples, we have:
[tex]OverripeApples=\frac{1}{3}(72)=24\\\\OverripeOranges=\frac{3}{5}(40)=24[/tex]
Hence, we have that there are 24 pieces of overripe oranges and 24 pieces of overripe apples. It means that there is a total of 48 overripe fruit.
Have a nice day!