Solve for p:
3 + p < 10
Answer:
p < 7
Step-by-step explanation:
To isolate the p, subtract 3 from both sides to get p < 7.
The correct answer is p < 7
Explanation:
To get your answer you need to first set out you equation, 3 + p < 10. Next, you need to subtract 3 from both sides of the equation, 3 + p - 3 < 10 - 3 = p < 7. Finally, we have our answer of p < 7.
Hope This Helps!!!
-AnimeDabGirl
A positive real number is 6 less than another. If the sum of the square of the two numbers is 38, then finds the numbers.
Answer:
There seems to be a typo error but still this has solution.
Let the number be = x
A positive real number is 6 less than another. Means the second will be [tex](x+6)[/tex]
The sum of the square of the two numbers is 38.
[tex]x^{2} +(x+6)^{2} =38[/tex]
=> [tex]x^{2} +36+12x+x^{2} =38[/tex]
=> [tex]2x^{2}+12x+36 =38[/tex]
=> [tex]2x^{2}+12x=2[/tex]
=> [tex]2x^{2}+12x-2=0[/tex]
Taking out 2 common;
=> [tex]x^{2}+6x-1=0[/tex]
Solving this quadratic equation, we get;
[tex]x=-3+\sqrt{10}[/tex] and [tex]x=-3-\sqrt{10}[/tex]
As positive number is needed, we have [tex]-3+\sqrt{10}[/tex]
or x = [tex]\sqrt{10}-3[/tex]
x = 0.162277
And other number is 6.162277.
Given:
A positive real number is 6 less than another. The sum of the square of the two numbers is 38.Question:
Find out the numbers.
Problem-solving:
Let us use [tex]\boxed{ \ x \ }[/tex] to represent the positive real number.
This positive real number is 6 less than another. The other number is [tex]\boxed{ \ x + 6 \ }[/tex]
The sum of the square of the two numbers is 38, i.e., [tex]\boxed{ \ x^2 + (x + 6)^2 = 38 \ }[/tex]
Let us work on expanding it.
[tex]\boxed{ \ x^2 + (x + 6)^2 = 38 \ }[/tex]
Recall that [tex]\boxed{ \ (a + b)^2 = a^2 + 2ab + b^2 \ }[/tex]
[tex]\boxed{ \ x^2 + x^2 + 12x + 36 = 38 \ }[/tex]
[tex]\boxed{ \ 2x^2 + 12x + 36 - 38 = 0 \ }[/tex]
[tex]\boxed{ \ 2x^2 + 12x - 2 = 0 \ }[/tex]
Both sides are divided by two.
[tex]\boxed{ \ x^2 + 6x - 1 = 0 \ }[/tex]
Let us solve the equation by using the quadratic formula.
[tex]\boxed{ \ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \ }[/tex]
a = 1b = 6c = -1[tex]\boxed{ \ x = \frac{-6 \pm \sqrt{6^2 - 4(1)(-1)}}{2(1)} \ }[/tex]
[tex]\boxed{ \ x = \frac{-6 \pm \sqrt{36 + 4}}{2} \ }[/tex]
[tex]\boxed{ \ x = \frac{-6 \pm \sqrt{40}}{2} \ }[/tex]
[tex]\boxed{ \ x = \frac{-6 \pm 2\sqrt{10}}{2} \ }[/tex]
[tex]\boxed{ \ x = \frac{-6}{2} \pm \frac{2\sqrt{10}}{2} \ }[/tex]
[tex]\boxed{ \ x = -3 \pm \sqrt{10} \ }[/tex]
[tex]\boxed{ \ x_1 = -3 + \sqrt{10} \ . \ . \ . \ x_1 > 10 \ }[/tex] this is fulfilled.
[tex]\boxed{ \ x_2 = -3 - \sqrt{10} \ . \ . \ . \ x_2 < 10 \ }[/tex]
Thus, the positive real number is [tex]\boxed{ \ x = -3 + \sqrt{10} \ }[/tex]The other number is [tex]\boxed{ \ (-3 + \sqrt{10}) + 6 \rightarrow \boxed{ \ 3 + \sqrt{10} \ }}[/tex][tex]\boxed{ \sqrt {10} = 3.162 \ }[/tex]
Therefore [tex]\boxed{ \ x = -3 + 3.162 \rightarrow \boxed{ \ 0.162 \ }}[/tex]And the other number is [tex]\boxed{ \ 0.162 + 6 \rightarrow \boxed{ \ 6.162 \ }}[/tex]Notes:
[tex]\boxed{ \ ax^2 + bx + c = 0, \ \ \ \ \ a \neq 0 \ }[/tex] is a quadratic equation in standard form.
x is a variable a, b, and c are real number coefficientsMethods of solving quadratic equations include:
Factoring and using the zero product property: [tex]\boxed{ \ (x - a)(x - b) = 0 \ } \ if \ and \ only \ if \ \boxed{ \ (x - a) = 0 \ or \ (x - b) = 0 \ }[/tex]Using the square root property: [tex]\boxed{ \ x^2 = a, \ then \ x = \pm \sqrt{a} \ }[/tex]Completing the square: [tex]\boxed{ \ x^2 + bx + \bigg({\frac{b}{2}} \bigg)^2 = \bigg( x + \frac{b}{2} \bigg)^2 \ }[/tex]Using the quadratic formula: [tex]\boxed{ \ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \ }[/tex]Learn moreFactoring methods https://brainly.com/question/2568692What is the y-intercept of the quadratic function f(x) = (x – 6)(x – 2)? https://brainly.com/question/1332667What are the coordinates of the vertex of the graph? https://brainly.com/question/1286775Keywords: a positive real number is 6, less than another, if the sum of the square, 38, then finds, quadratic equation, methods, factoring, the zero product property, the square root, completing, the quadratic formula
Two triangles have altitudes of equal length. if the areas of these triangles have a ratio of 3:4 then the bases of the triangles have the ration of what?
show work pleaseeee
Final answer:
The bases of the triangles have a ratio of 3:4.
Explanation:
The areas of two triangles with equal altitudes have a ratio of 3:4. We can set up the equation:
A₁/A₂ = 3/4
Let's denote the bases of the triangles as b₁ and b₂. The formula for the area of a triangle is A = (1/2) * base * height. Since the altitudes are equal, we can write:
A₁ = (1/2) * b₁ * h
A₂ = (1/2) * b₂ * h
Substituting these equations into the ratio, we get:
(1/2) * b₁ * h / (1/2) * b₂ * h = 3/4
Cancelling out the height and simplifying, we find:
b₁ / b₂ = 3/4
Therefore, the bases of the triangles have a ratio of 3:4.
write the standard form of the equation of the line through the given point with the given slope THROUGH:(1,2), slope =7, 50 POINTS
The equation of line passes through the point (1, 2) will be;
⇒ y = 7x - 5
What is Equation of line?The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
The point on the line are (1, 2).
And, The slope is,
⇒ m = 7
Now,
Since, The equation of line passes through the point (1, 2).
And, Slope of the line is,
⇒ m = 7
Thus, The equation of line with slope 7 is,
⇒ y - 2 = 7 (x - 1)
⇒ y - 2 = 7x - 7
⇒ y = 7x - 7 + 2
⇒ y = 7x - 5
Therefore, The equation of line passes through the point (1, 2) will be;
⇒ y = 7x - 5
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PLEASE I BEG YOU TOO HELP ME OR ELSE IM GOING TK FAIL MY CLASS
Explanation: For questions 4-11, plug in the values of the variables into the equations. Ex no. 8: 7.8 + 3.5(w) where w=6.8. Plug 6.8 into the equation: 7.8 + 3.5(6.8) = 7.8 + 23.8 = 31.6 is the answer.
For questions 12-15, the order of operations is Please Excuse My Dear Aunt Sally: Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction. In other words, solve each equation according to the arrangement of the operations. Ex no. 15: y² - 10 ÷ 5 + x where x = 2.5 and y = 4. Plug these numbers into the equation: 4² - 10 ÷ 5 + 2.5. The order of operations says that parenthesis should be solved first. Since there are no parenthesis, we can skip this operation. The next operation is exponents. 4² has an exponent of 2, which means that we multiply 4 by itself 2 times to get 16 (4 x 4 = 16). We now have 16 - 10 ÷ 5 + 2.5. The next operation is multiplication. There is no multiplication in this equation, so we skip this operation. Next is division. We can divide -10 by 5 to get -2. We now have 16 - 2 + 2.5 (Do not change an addition sign unless you are dividing a negative number by a positive number). The next operation is addition. We can add -2 and 2.5 to get 0.5. Lastly, we can also add 16 by 0.5: 16 + 0.5 = 16.5 is the answer.
mrs. barney earns $80 for tutoring for 2 hours. If she gets a 10% raise, how much does she now earn per hour.
please show work
Answer:$88
Step-by-step explanation:
multiply 80 dollars by 10% then add that answer to 80 dollars and that gives you 88 dollars
how many solutions does the equation 2x-6=6+2x
Answer:
2 solutions
Step-by-step explanation:
Since the equations are not equal, they provide two solutions. Negative numbers provide no solutions. If they are equal to zero, they have one solution.
Answer:
Eliphat is right, 2
Step-by-step explanation:
witch ordered pair is the solution to the system of equations
{-5x-3y=12
{y=x-12
[tex]\left\{\begin{array}{ccc}-5x-3y=12&(**)\\y=x-12&(*)\end{array}\right\\\\\text{Substitute}\ (*)\ \text{to}\ (**):\\\\-5x-3(x-12)=12\qquad\text{use distributive property}\\-5x+(-3)(x)+(-3)(-12)=12\\-5x-3x+36=12\qquad\text{subtract 36 from both sides}\\-8x=-24\qquad\text{divide both sides by (-8)}\\\boxed{x=3}\\\\\text{Put the value of x to}\ (**):\\\\y=3-12\\\boxed{y=-9}\\\\Answer:\ \boxed{x=3\ and\ y=-9\to(3,\ -9)}[/tex]
To which set or sets does -20 belong?
A: whole number, integer and rational number
B: integer and rational number
C: negative integer
D:Whole number and integer
Answer:
B: integer and rational number
Step-by-step explanation:
whole numbers: 0, 1, 2, 3, 4, ...
integer: ..., -4, 3, -2, 1, 0, 1, 2, 3, 4, ...
rational number: any number that can be written as a fraction of integers
Answer: B: integer and rational number
Answer:
B and C.
Step-by-step explanation:
-20 is a negative integer.
It is also rational.
How much is 0.324 divided by 0.27
Answer:
The answer is 1.2
Step-by-step explanation:
Answer:
1.2
Step-by-step explanation:
You can use a calculator... Or you can ask google this, "What is 0.324 divided by 0.27?"
0.324 divided by 0.27 is 1.2
Factor -8x^3-2x^2-12x-3
[tex]-8x^3-2x^2-12x-3\\\\=-2x^2(4x+1)-3(4x+1)\\\\=(4x+1)(-2x^2-3)\\\\=\boxed{-(4x+1)(2x^2+3)}[/tex]
I WILL GIVE BRAINLYEST TO FIRST 7 PEOPLE TO ANSWER IN THE NEXT 10 MINUTES
last year austin texas received 23.5 inches of rainfall. this year , austin recieved 21.2 inches of rainfall find the percent of decrease in the number of inches of rainfall. round your answer to the nearest tenth of a percent, if necessary
Answer:
9.8 percent decrease
Step-by-step explanation:
To find the percent decrease, we take the original value and subtract the new value and divide by the original value.
percent decrease = (original - new)/ original
= (23.5 - 21.2)/ 23.5
=2.3/23.5
=.09787234
This is in decimal form. Multiply by 100 to put it in percent form
9.787234 percent
Round to the nearest tenth so we look at the 8 and round up.
9.8 percent decrease
Answer:
The answer is 9.8%
Step-by-step explanation:
Also, only two people can answer a question.
Please help!! What is the value of the following expression when x=3 and y= -2?
Answer:
20 is the answer.
Step-by-step explanation:
Substitute 3 in for x and -2 in for y.
4(3) - (-2 to the third power)
12 - -8 = 12 + 8
The answer is 20
Please mark brainliest as that would really help out :3
can√(a²+b²) be written as √(a+b)?????
Answer:
It can be written that way, but the functions are not the same. The numbers the would be plugged in would not produce the same answer.
9. Two lines that lie in parallel planes are _____ parallel. always never sometimes
Answer:
Sometimes
Step-by-step explanation:
Answer:
Two lines that lie in parallel planes are sometimes parallel.
Step-by-step explanation:
Two lines that lie in parallel planes are sometimes parallel. It is not necessary that they are always parallel.
Rather two parallel lines are always coplanar.
There is always a plane which contains two parallel lines.
The points with coordinates (x, -1), (2,2), and (4,3) lie on the same line. What is the value of x?
Find the slope of the line passing throught the points (2, 2) and (4, 3).
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
Substitute:
[tex]m=\dfrac{3-2}{4-2}=\dfrac{1}{2}[/tex]
If the point (x, -1) lie on the same line, then the slope of line passing through the points (2, 2) and (x, -1) the same:
Substitute:
[tex]m=\dfrac{-1-2}{x-2}=\dfrac{-3}{x-2}[/tex]
We have the equation:
[tex]\dfrac{-3}{x-2}=\dfrac{1}{2}[/tex] cross multiply
[tex](1)(x-2)=(-3)(2)[/tex]
[tex]x-2=-6[/tex] add 2 to both sides
[tex]x=-4[/tex]
Answer: x = -4.How do I write 2x-y=12 in slope intercept form
[tex]2x-y=12\\\\y=2x-12\\\\[/tex]
Shelly types 301 words in 3 1/2 minutes what is the rate at which Shelly types in words per minute?
Answer: " 86 words per minute "
______________________________________________
Step-by-step explanation:
______________________________________________
We are looking for the "unit rate" ; or "rate per [single] unit" ;
in this case, "words per [single} minute" ; that is "words per minute"
Given: "301 words per 3.5 minutes" ;
or: " 301 words / 3.5 min. " ;
= " (301 / 3.5) words/ min.
= " 86 words / min. "
_______________________________________________
The answer is: " 86 words per minute " .
_______________________________________________
Hope this helps!
Best wishes!
_______________________________________________
Marcus bought a $48 concert ticket through an online ticket broker. If the broker charged a 15% brokerage fee, how much did Marcus have to pay for the ticket?
Answer:
$55.20
Step-by-step explanation:
What is the brokerage fee
.15 * 48 = 7.2
The total cost of his ticket is the price of the ticket plus the brokerage fee
total cost = 48 + 7.2
= $55.20
Marcus had to pay a total of $55.20 for the concert ticket, which includes the 15% brokerage fee on top of the original ticket price.
Explanation:Marcus bought a concert ticket for $48. The online ticket broker charged a 15% brokerage fee on top of the ticket price. To calculate the total amount Marcus had to pay, we first need to calculate the brokerage fee. The brokerage fee is found by multiplying the ticket's price by the brokerage fee rate. So, $48 multiplied by 15% (or 0.15) gives us the brokerage fee of $7.20. This brokerage fee is then added back to the original ticket price, so Marcus paid a total of $48 + $7.20 = $55.20 for the concert ticket.
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Which of the following word problem can be solved using the equation 4(x+8)=40
Answer:
The answer would be x=2
Step-by-step explanation:
Find the perimeter and area of the polygon shown below. The polygon is a trapezoid made up of a rectangle and a right triangle. The rectangle is 20 feet long and 15 feet wide. The right triangle joins the rectangle at a side that is 15 feet wide, and this is the height of the triangle. The base of the triangle is 8 feet and the hypotenuse is 17 feet.
The perimeter of the polygon is 110 feet and the area is 360 square feet.
Explanation:The polygon consists of a rectangle and a right triangle. To find the perimeter, we add the lengths of all sides. The length of the rectangle is 20 feet and its width is 15 feet, so the perimeter of the rectangle is 2 * (20 + 15) = 70 feet. The length of the base of the right triangle is 8 feet and the hypotenuse is 17 feet. The other side of the triangle is the height, which is given as 15 feet. Therefore, the perimeter of the polygon is 70 + 8 + 15 + 17 = 110 feet.
To find the area, we calculate the area of the rectangle and the triangle separately and then add them together. The area of the rectangle is length * width = 20 * 15 = 300 square feet. The area of the right triangle is 0.5 * base * height = 0.5 * 8 * 15 = 60 square feet. Therefore, the area of the polygon is 300 + 60 = 360 square feet.
In each family of functions, the function is the most basic function in the family
Answer:
I think it would be linear because its really easy?!
Step-by-step explanation:
which of the following is the same as 2.3 x 10^3?
a) .23
b) 230
c) .023
d) 2,300
The answer is D you move the decimal over 1 then add 2 0
Answer:
D
Step-by-step explanation:
Jayla ate 75% of the jelly beans in the bag. If she ate 24 jelly beans how many were in the bag?
Answer:
32 jelly beans were in the bag
Step-by-step explanation:
We know 75% is 3/4 and that she ate 24, so divide 24 by 3 then multiply it by 4:
24/3= 8
8 x 4 = 32
Final answer:
By dividing the number of jelly beans Jayla ate (24) by 75% and scaling it up to 100%, we determine that the bag initially contained 32 jelly beans.
Explanation:
Jayla ate 75% of the jelly beans in the bag, which equaled 24 jelly beans. To find out how many jelly beans were in the bag originally, we need to find what amount corresponds to 100% if 75% is 24 jelly beans. We perform this calculation by dividing the amount eaten (24 jelly beans) by the percentage she ate (75%), and then multiplying by 100% to scale it up to the total amount.
The calculation goes as follows: (24 / 0.75) = 32. This means there were originally 32 jelly beans in the bag before Jayla ate any.
In a recent international sport competition, the top three countrieslong dash—Country A, Country B, and Country Clong dash—won a total of 119119 medals. Country B won 1111 more medals than Country C. Country A won 3737 more medals than the total amount won by the other two. How many medals did each of the top three countries win?
Answer:
Country A won 78 medals
Country B won 26 medals
Country C won 15 medals
Step-by-step explanation:
We have been given with :-
A+B+C=119 _____equation(1)
B=C+11 ____equation(2)
A=B+C+37 ____equation(3)
1) Starting with the 3rd equation,
A=B+C+37
2) Subtract 37 from both sides
A-37=B+C+37-37
3) Cancelling out +37 and -37 from the right side we get,
A-37 = B+C
or
B+C = A-37
4) Plugin B+C= A-37 in the equation 1,
A+B+C = 119
=> A+(A-37) = 119
=> 2A-37 = 119
5) Add 37 to both sides
2A-37+37=119+37
6) Cancelling out -37 and +37 from the left side, we get
2A = 156
7) Divide both sides by 2
[tex]\frac{2A}{2} =\frac{156}{2}[/tex]
8) Cancelling out the 2's on the left side, we get
A = 78
9) Now, we plugin A=78 in the equation 1
A+B+C=119
=> 78+B+C=119
10) Subtract 78 from both sides
78+B+C-78 = 119 -78
11) Cancelling out +78 and -78 from the left side, we get
B+C= 41 ____let it be equation (4)
12) Subtracting C from both the sides of the equation 2, we get
B=C+11
=> B-C = C+11 - C
13) Cancelling out +C and -C from the right side, we get
B-C= 11 _____let it be equation (5)
14) Adding the equations 4 and 5, we get
B+C+B-C=41+11
15) Cancelling out the +C and -C, we get
2B = 52
16) Divide both sides by 2
[tex]\frac{2B}{2}=\frac{52}{2}[/tex]
17) Cancelling out the 2's on the left, we get
B = 26
18) Substituting A= 78 and B= 26 in the equation (1), we get
A+B+C=119
=> 78+26+C=119
=> 104+C=119
19) Subtracting 104 from both the sides, we get
104 + C - 104 = 119 -104
20) Cancelling out +104 and -104 from the left side, we get
C = 15
The problem is a basic algebra problem where we assign variables to the number of medals each country won. We then use given equations related to these variables to solve for each unknown.
Explanation:In this problem, we are trying to solve for the number of medals each country won, so let's start by assigning variables for the number of medals for each country. Let's say, Country A = A, Country B = B, and Country C = C.
According to the problem, we know that Country A won 37 more medals than the sum of the other two countries, that's expressed by this equation: A = B + C + 37.
It's also stated that Country B won 11 more medals than Country C, so we have this equation: B = C + 11.
Further, we know that the total number of medals is 119, so we have this equation: A + B + C = 119.
Now, solve these equations systematically. First, substitute the value of A and B from first and second equation into the third equation and solve the variable C, then substitute the obtained value of C in second equation to find B and finally substitute the obtained values of B and C in first equation to find A.
This is a basic algebraic problem-solving situation. It involves the use of equations and variables to find the solution.
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Write an equation of the line that passes through the points (1,1) (5,9)
Answer:
y = 2x - 1
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 )
To find m use the gradient formula
m = ( y₂ - y₁ ) / ( x₂ - x₁ )
with (x₁, y₁ ) = (1, 1) and (x₂, y₂ ) = (5, 9)
m = [tex]\frac{9-1}{5-1}[/tex] = [tex]\frac{8}{4}[/tex] = 2
y = 2x + c ← is the partial equation
To find c substitute either of the 2 points into the partial equation
using (1, 1 ), then
1 = 2 + c ⇒ c = 1 - 2 = - 1
y = 2x - 1 ← equation of line
help me understand this question
Answer:
m∡J = 110°, m∡L = 45°, m∡K = 25°
Step-by-step explanation:
Similar means they have the same angles. F corresponds with K, G with J, and E with L.
m∡J = 110° because it corresponds with m∡G.
m∡L = 45° because it corresponds with m∡E.
To get m∡K, we have to remember all triangles add to 180. Add J and L together, and subtract that sum from 180° to get m∡F, which is equal to m∡K.
110 + 45 = 155
180 - 155 = 25
m∡K = 25°
Help plz with this problems
To find the perpendicular slope, we simply flip the fraction (aka reciprocal) and flip the sign (go from positive to negative, or vice versa)
So for problem 1a) we flip the fraction to go from 4/3 to 3/4. Then we flip the sign to go from +3/4 to -3/4. The final answer to problem 1a) is -3/4
The answer to problem 1b) is 7/3 following the same basic steps: -3/7 ---> -7/3 ---> 7/3
The answer to problem 1c) is -1/4. You can think of 4 as 4/1 which flips to 1/4 and it becomes -1/4
I'll let you try out the rest 1d and 1e. Tell me what you get so I can check your answers.
Please answer and explain these 3 questions. Thank you!
Use the distributive property to simplify the expression 25(x-y)
25(x-y) simplified using the distributive property gives us 25x - 25y.
WE are given the expression as 25x-25y
WE know that distributive property states that an expression of the form A(B + C) can be solved by a multiplication over addition operation that is
A(B + C) = AB + AC
To use the distributive property to simplify 25(x-y), we need to distribute the 25 to both x and y separately.
So,
25(x-y) = 25(x) - 25(y)
= 25x - 25y
Therefore, 25(x-y) simplified using the distributive property gives us 25x - 25y.
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Final answer:
The expression 25(x-y) is simplified using the distributive property by multiplying 25 by each term inside the parentheses, resulting in 25x - 25y.
Explanation:
To use the distributive property to simplify the expression 25(x-y), you should multiply each term inside the parentheses by 25.
This is what it looks like when we apply the distributive property:
25 × (-y) = -25y
So, the simplified expression is 25x - 25y.
When we evaluate expressions, we are typically trying to express them in a way that shows the multiple or product terms explicitly. This process is like reversing distributive law and turning it back into factors (multiples). Here, the distributive law helps us see that the expressions 25x and -25y, when combined, produce the same value as the original expression 25(x-y).