Answer:
x = 2a
Step-by-step explanation:
a(x - a) = a² ( divide both sides by a )
x - a = a ( add a to both sides )
x = 2a
Answer:
x = 2a
Step-by-step explanation:
Given equation
[tex]\sf a(x-a)=a^2[/tex]
Make x the subject
expand brackets:
[tex]\sf \implies ax-a^2=a^2[/tex]
Add [tex]\sf a^2[/tex] to both sides:
[tex]\sf \implies ax-a^2+a^2=a^2+a^2[/tex]
[tex]\sf \implies ax=2a^2[/tex]
Divide both sides by a:
[tex]\sf \implies \dfrac{ax}{a}=\dfrac{2a^2}{a}[/tex]
[tex]\sf \implies x=2a[/tex]
Final solution
[tex]\sf x=2a[/tex]
In ΔOPQ, the measure of ∠Q=90°, OQ = 24, QP = 7, and PO = 25. What is the value of the tangent of ∠O to the nearest hundredth?
Answer: 0.29
Step-by-step explanation:
OQ is the side opposite angle P, QP is the side opposite angle O, and PO is the side opposite angle Q.
This means that tangent = opposite/adjacent, the tangent of angle O is the opposite side, QP, over the length of the adjacent side, OQ. (It cannot be PO since that's the hypotenuse)
This means that the tangent of O is 7/24, which is about 0.29
Anthony takes out a student loan to pay for his college tuition this year. Find the interest on the load if he borrowed $6,000 at an annual interest rate of 6% for 15 years
Answer:
the interest would be $5,400 after 15 years
A function f is defined by f(x, y) = 3x2 – 4y. What is the value of
f(3, 2)?
Assuming the function is [tex]f(x,y)=3x^2-4y[/tex]
--> then f(3,2) is: [tex]f(3,2) = 3(3^2)-4(2)=3*9-8=27-8=19[/tex]
Hope that helps!
1) Consider the two functions. Which statement is true?A) The rate of change for function A and function B are the same.B) The slope of function B is negative and the slope of function A is positive.C) The rate of change for function A is greater than the rate of change for function B.D) The rate of change for function B is greater than the rate of change for function A
Answer:
B.
Step-by-step explanation:
If two triangles are congruent, which of the following statements must be
true? Check all that apply.
A. The triangles have the same size, but not the same shape.
B. The corresponding sides of the triangles are congruent.
I c. The corresponding angles of the triangles are congruent.
D. The triangles have the same size and shape.
B. The corresponding sides of the triangles are congruent.
I c. The corresponding angles of the triangles are congruent.
D. The triangles have the same size and shape.
Step-by-step explanation:
.
Unit 4: Congruent Triangles Homework 2: Angles of Triangles
The value of the third angle that can be found in the information given about the congruent triangles will be 45°.
How to solve the triangle?From the complete information, the angles that are given in the triangle are 76° and 59°.
It should be noted that the value of the total angles that are in a triangle is 180°. Therefore, the value of the last angle will be:
= 180° - (76° + 59°)
= 180° - 135°
= 45°
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In Art Museum has 1042 pictures to split equally into 35 different exhibits. How many more pictures does the museum need to make sure each Exhibit
Has the same amount
Answer:
8 more pieces
Step-by-step explanation:
First, divide 1042 by 35 to get 29 and 27/35. Since each exhibit needs 35 pieces, and since 35- 27 is 8, the museum needs 8 more pieces.
Hopefully this helps- let me know if you have any questions!
Ben has agreed to play fewer video games and spend more time studying. He has agreed to play less than 10 hours of video games each week. On Monday through Thursday, he plays video games for a total of 5 1/2 hours. For the remaining 3 days, he plays video games for the same amount of time each day. Find t, the amount of time he plays video games, for each of the 3 days.
Answer:
t < 1.5
Step-by-step explanation:
Mon-Thu: 5.5 hours
each of the remaining 3 days: t hours each day
total time: 3t + 5.5
The total time must be less than 10 hours.
3t + 5.5 < 10
3t < 4.5
t < 1.5
Please help! locks in 30 min!
Is (3, 1) a solution to this system of equations?
3x + 3y = 12
12x + y = 13
Yes or no
Answer: No
Step-by-step explanation:
(3,1) is not a solution because when plugging in x=3 and y=1 to the second equation, you get: 12(3) + 1 = 13 → 36 + 1 = 13 → 37 = 13, which is false.
Use a diagram to show that (3x+1)(x+2) is equivalent to 3x2+7x+2.
What is the poh of a solution of hno3 that has [oh– ] = 9.50 × 10–9 m? round to the nearest hundredth.
The hydroxide-ion concentration or pOH of HNO₃ solution comes to be 8.02.
What is the pOH of the solution?The pOH of a solution is the negative logarithm of the hydroxide-ion concentration.
or pOH = -log[OH⁻]
The hydroxide-ion concentration OH⁻ of HNO₃ solution = 9.5 * 10⁻⁹ million.
So, the pOH of the HNO₃ solution =-log[9.5* 10⁻⁹] = 8.02
Therefore, the hydroxide-ion concentration or pOH of HNO₃ solution comes to be 8.02.
To get more about pH and pOH visit:
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Answer:
8.02
Step-by-step explanation:
trust
Please help me ASAP
Answer:
12 -9
Step-by-step explanation:
Look to the ends of each arrow and you will see each number the arrow is on. Hope this helps.
Answer:
[tex]y=-x+3[/tex]
Step-by-step explanation:
Let's start by defining what slope-intercept form is. Slope-intercept form is:
y=mx+b
Where...
"y" = y-coordinate of any point on the line
"m" = slope of the line
"x" = x-coordinate of any point on the line
"b" = y-intercept (where the line intercepts the y-axis)
Let's start by finding the y-intercept. As stated above, the y-intercept is where the line intercepts the y-axis. Looking at the graph, we can tell that in this case, it is (0, 3).
Note that the y-intercept (b) is represented by ONLY the y-value, which in this case is 3.
Now, let's find the slope. Start by taking ANY two points on the line. Let's use (0, 3) and (1, 2).
The formula for slope is:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]y_1, y_2:$ Values for the two y-coordinates\\x_1, x_2:$ Values for the two x-coordinates[/tex]
Substitute the given points into the equation:
[tex]m=\frac{2-3}{1-0}=\frac{-1}{1}=-1[/tex]
The slope is -1.
Finally, we substitute our slope and y-intercept back into the equation and get:
[tex]y=-x+3[/tex]
If you were to buy a $1,000 computer in Tennessee, how much would it cost in
Williamson County? How much would you save if you bought it in Davidson County?
This refers to the tax paid to a governing body for the sales of certain goods and services.
In Williamson County, the sales tax rate is 9.75% = 9.75% × $1,000 = $1,097.5
In Davidson County , the sales tax rate is 9.25% = 9.25% × $1,000 = $1,092.5
The amount saved will therefore be $1,097.5 - $1,092.5 = $5.
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Describe how to find the sale price of an item that has been discounted 15%.
Answer:
Convert 15% to a regular number by moving the decimal 2 times to the left so 15.0 becomes 0.15 then do 0.15 × the original price, then take the original price and subtract the amount you got from doing 0.15 × the original price
Describe the transformation to the parent to the parent function
y = -2|x+3|-1
Transformation:
Using translation concepts, it is found that the parent function was reflected over the x-axis, vertically stretched by a factor of 2, shifted left 3 units and down 1 unit.
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
The parent function is:
y = |x|
The translations are as follows:
It was multiplied by -2, hence it was vertically stretched by a factor of 2, and since it was multiplied by a negative number, reflected over the x-axis.x -> x + 3, hence it was shifted 3 units right.One was subtracted from the function, hence it was shifted one unit down.More can be learned about translation concepts at https://brainly.com/question/4521517
For each set of three lengths, determine if they can be the side lengths of a triangle.
Answer:
Yes, No, Yes, NoStep-by-step explanation:
Use the triangle inequality theorem, which states that the sum of any two side lengths must be greater than the third side length.
Apply this to each combination.
Use one inequality, compare the sum of smallest two sides with the largest side.
1) 4, 9, 8
4 + 8 = 12 > 9, so Yes2) 7, 25, 7
7 + 7 = 14 < 25, so No3) 8.8, 24, 15.8
8.8 + 15.8 = 24.6 > 24, so Yes4) 5, 9, 3
3 + 5 = 8 < 9, so NoWhat is the formula of the curved surface of a cylinder?
Answer:
2πr × h = 2πrh
Step-by-step explanation:
that is the formula for a curved surface of a cylinder 2πr × h = 2πrh.
Please help me!! I will mark you brainliest!
Answer:
Step-by-step explanation:
Right off the bat, you will know the lowest number is 52 and the highest number is 65, therefore there will act as the guides for your box and whisker plot. This eliminates answers B and C because they are not accurate to that.
Next, we find the median of the set of numbers by crossing out (writing it down, or imagining doing so) the numbers on either end consecutively to until you reach the center number, ours being 58. This eliminates answer A.
This leads us to belive answer D is the correct box and whisker plot.
How long is 10% of a 24-hour day?
Answer:
2.4 hour is 10%
Step-by-step explanation:
Because 10% is equal to 0.1 24÷ 10% =2.4
Directions: Find each missing measure. 1.
Answer:
1. 19 Degrees
2. 63 Degrees
3. 37 Degrees
4. 119 Degrees
5. 69 Degrees
6. 71 Degrees
7.1 65 Degrees
7.2 48 Degrees
7.3 42 Degrees
Step-by-step explanation:
Angles in a triangle always add up to 180 degrees. (180-79-82=19 for the first one)
The little box in a triangle represent 90 degrees.
7.2 Vertical Angles are equal to each other
Choose the student who wrote and solved the equation correctly.
The cost of 4 bananas is $2.36. What is the cost of each banana?
Using proportions, it is found that the cost of each banana is of $0.59, and Juan is the student who wrote and solved the equation correctly.
What is a proportion?A proportion is a fraction of a total amount.
In this problem, the cost of 4 bananas is $2.36, hence the cost of each banana is given by:
C = $2.36/4 = $0.59.
Which means that Juan is correct.
More can be learned about proportions at https://brainly.com/question/24372153
use the intersect method to solve the equation
-2x+1=-x^2+4
The intersect method involves spliting an equation to a system of equations
The solutions to the equation are (-1, 3) and (3,-5)
How to solve the equation?The equation is given as:
-2x + 1 = -x^2 + 4
Using the intersect method, we have the following equations
y = -2x + 1
y = -x^2 + 4
Next, we plot the graph of both equations
From the graph (see attachment), we have the following points of intersection
(x,y) = (-1, 3) and (3,-5)
Hence, the solutions to the equation are (-1, 3) and (3,-5)
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Which expression is equivalent to (q^6)^2
○ q^3
○ q^8
○ q^12
○ q^36
btw, its not q^36
Please help I will give brainliest.
Answer:
3 Rd one
Step-by-step explanation:
donee....!!✓give me the branliest
ABC and AED are straight lines.
BE and CD are parallel.
A
B
AD = 10.5 cm
AE = 4.2 cm
BE = 2.9 cm
a) Work out length CD.
AC = 8.75 cm
b) Work out length BC.
Answer:
a) CD = 7.25
b) BC = 5.25
Step-by-step explanation:
a)The parallel lines mean the triangles are similar. ΔADC ~ ΔAEB. Corresponding sides are proportional, so ...
AD/AE = DC/EB
10.5/4.2 = CD/2.9
CD = 2.9(5/2) = 7.25
__
b)Corresponding sides are proportional, so ...
BC/AC = ED/AD
BC = AC(ED/AD) = 8.75(10.5 -4.2)/10.5 = 8.75(3/5) = 5.25
Jean wants to put furniture in her clubhouse. She drew a floor plan of the clubhouse, as shown. Each grid unit represents one foot.
PLEASE HELP ME
Answer:
hexagon24 ft of baseboardStep-by-step explanation:
1.You have correctly counted the 6 sides of the figure. A 6-sided polygon is a hexagon.
__
2.The length of baseboard needed is the length of the perimeter of the figure. That length is the sum of the side lengths. Starting from the lower left corner and working clockwise, the side lengths are ...
1 ft + 5 ft + 2 ft + 1 ft + 5 ft + 10 ft = 24 ft
24 feet of baseboard are needed.
__
Additional comment
The area of the figure can be found several ways. One of them is to subtract the corner cutout area from the overall rectangle area. The overall rectangle is 10 ft wide and 4 ft high, for an area of (10 ft)(4 ft) = 40 ft². The upper left triangle cutout is 4 ft wide and 3 ft high, for an area of (1/2)(4 ft)(3 ft) = 6 ft². The upper right trapezoid cutout has bases of 1 ft and 4 ft, and a height of 4 ft, so its area is 1/2(1 ft +4 ft)(4 ft) = 10 ft².
Then the clubhouse area is 40 ft² -6 ft² -10 ft² = 24 ft².
PLSS help this is important
(will give brainliest)
Answer:
A (first one)
Step-by-step explanation:
From T to T' you add 2 to the x and subtract 3 from the y
Then you do that to the x and y on O and Y
So for O, -4+2 is -2 and 1-3=-2
then you just do that for Y and you get (0,0) when applied
A circular rug has a circular table in the middle. The diameter of the rug is 12 meters and the diameter of the table is 4 meters. What area of rug is left after placing the table over the midddle of the rug? Use 3.14
Answer:
100.53m² area of carpet is left after putting the table in place.
What classification is the following expression?
Answer:
Types of algebraic expressions may further be distinguished in the following five categories. They are: monomial, polynomial, binomial, trinomial, multinomial. 1. Monomial: An algebraic expression which consists of one non-zero term only is called a monomial.
Step-by-step explanation:
1+1=2