Let the balance = Y and the number of weeks = x
She takes out 15 per week, so multiply 15 by x ( the number of weeks) to get 15x.
You would then want to subtract that from the amount she started with in her account.
The equation becomes: Y = 150 - 15x
how to create an equation with infinitely many solutions.
Answer:
See below.
Step-by-step explanation:
An equation with infinite solutions is, strictly, an identity.
An example is 2(x + 3) = 4x + 6
Simplifying we get 4x + 6 = 4x + 6. We can replace by any value of x and the equation will hold true.
WILL GIVE BRAINLIST WHEN I CAN the answer is not 72 or 54!!
Answer:
x = 20°
Step-by-step explanation:
In a circle, the measure of an inscribed angle is half the measure of the intercepted arc.
x = 40/2 = 20°
A scientist has two solutions, which she has labeled Solution A and Solution B. Each contains salt. She knows that Solution A is 20% salt and
Solution B is 80% salt. She wants to obtain 180 ounces of a mixture that is 30% salt. How many ounces of each solution should she use?
The scientist should use 90 ounces of Solution A and 90 ounces of Solution B to get the desired mixture.
To obtain 180 ounces of a 30% salt mixture, the scientist should use 90 ounces of Solution A (20% salt) and 90 ounces of Solution B (80% salt) by solving a system of two equations.
To solve the problem, we need to create a system of equations based on the quantities of salt in each solution and the desired final mixture. We want to mix Solution A (20% salt) and Solution B (80% salt) to get 180 ounces of a mixture that is 30% salt. Let the amount of Solution A be x ounces and the amount of Solution B be y ounces.
The two equations representing the system are:
Equation for total mixture: x + y = 180 (total ounces of the mixture)Equation for salt content: 0.20x + 0.80y = 0.30 *180 (total ounces of salt in the mixture)Now, we solve this system of equations. Multiplying the second equation by 100 for simplicity, we get:
20x + 80y = 54 * 100
Using the first equation to express y in terms of x, we get y = 180 - x. Substitute y into the second equation:
20x + 80(180 - x) = 5400
Opening parentheses and simplifying gives us:
20x + 14400 - 80x = 5400
Subtract 20x from each side:
-60x + 14400 = 5400
Solving for x, we find that:
x = (14400 - 5400) / 60 = 90
Substituting x into y = 180 - x, we get y = 180 - 90 = 90.
Therefore, the scientist should use 90 ounces of Solution A and 90 ounces of Solution B to get the desired mixture.
Hershel’s bakery sells donuts by the box there are d donuts in each box Beverly is going to buy 10 boxes for a class trip. Which expression represents the total number of donuts that beverly is going to get for her field trip?
A. 10 x d
Explanation :
1 box has d donuts. So that equation would be 1 x d. 10 boxes has d donuts. So that equation would be 10 x d.
Answer:
A
Step-by-step explanation:
If f(x) = x/1 + x, what is the value of f(x+h)
Answer:
[tex]f(x+h)=\frac{x+h}{1+x+h}[/tex]
Step-by-step explanation:
Given function is:
f(x) = x/1 + x
In order to find f(x+h) we have to put x+h in place of x
[tex]f(x)=\frac{x}{1+x} \\f(x+h)=\frac{x+h}{1+x+h}[/tex]
Therefore,
[tex]f(x+h)=\frac{x+h}{1+x+h}[/tex]
Answer: B
Got it right lol
what is the value of the expression g * (g+1)^2 for g=2
Answer:
18Step-by-step explanation:
[tex]\text{Put}\ g=2\ \text{to the expression}\ g(g+1)^2:\\\\2(2+1)^2=2(3)^2=2(9)=18[/tex]
A data set with less variation will have a smaller ____________________.
A. minimum
B. mean
C. interquartile range
D. median
Answer: Option C
A data set with less variation will have a smaller __ interquartile range__.
Step-by-step explanation:
The datasets that have less variation are those that have smaller dispersion or variation measures.
Some of these measures of variance are variance, standard deviation, mean absolute deviation, range and interquartile range. Among the options shown, the only one that is used as a measure of variation is the interquartile range. The interquartile range is the difference between the third quartile and the first quartile of a data distribution. In other words, the interquartile range measures the range between the central 50% of the data.
Then the answer is the option C
!PLEASE HELP!
y + x = 3
Does the line increase or decrease? How do I find this without graphing the line?
Answer:
Decreasing
Step-by-step explanation:
y=mx+b is called slope-intercept from because it tells you the slope,m, and the y-intercept,b.
If the slope is positive then the line is increasing.
If the slope is negative then the line is decreasing.
If the slope is zero then the line is horizontal or constant.
So let's solve our equation for y:
y+x=3
Subtract x on both sides:
y=-x+3
The slope is -1.
Therefore the line is decreasing.
just a quick addition to @Freckledspots' great reply above.
y + x = 3
y = 3 - x
if we pick any random "x" value, and then pick another value larger than the one before for "x", to get a "y" value, if "y" is decreasing, the the first value of "y" will be larger, else it's increasing, let's do so, say using hmmm x = 2 and x = 7.
x = 2
y = 3 - 2
y = 1
x = 7
y = 3 - 7
y = -4
as "x" moves to the right, from 2 to 7, "y" moved down, from 1 to -4, thus is decreasing.
what is the surface area of the rectangular pyramid
Answer:
41.74 m²Step-by-step explanation:
We have:
rectangle 4.8 m × 3.8 m
two triangles with base b = 4.8 m and height h = 2.6 m
two triangle with base b = 3.8 m and height h = 2.9 m.
The formula of an area of a rectangle l × w:
[tex]A = lw[/tex]
Substitute:
[tex]A_1 = (4.8)(3.8) = 18.24\ m^2[/tex]
The formula of an area of a triangle:
[tex]A=\dfrac{bh}{2}[/tex]
Substitute:
[tex]A_2=\dfrac{(4.8)(2.6)}{2}=6.24\ m^2\\\\A_3=\dfrac{(3.8)(2.9)}{2}=5.51\ m^2[/tex]
The Surface Area:
[tex]S.A.=A_1+2A_2+2A_3\\\\S.A.=18.24+2(6.24)+2(5.51)=41.74\ m^2[/tex]
Answer:
GIVE THE OTHER DUDE BRAINLISET
Step-by-step explanation:
(6x - 9 - 2x)(8 + 5x - 5)
-27 - 33x + 20x²
Combine like-terms in all sets of parentheses and just FOIL it:
[4x - 9][5x + 3]
F - Multiply the first terms in each set of parentheses FARTHEST TO THE LEFT
O - Multiply the first term in the first set of parentheses FARTHEST TO THE LEFT by the last term in the second set of parentheses FARTHEST TO THE RIGHT
I - Multiply the last term in the first set of parentheses FARTHEST TO THE RIGHT by the first term in the second set of parentheses FARTHEST TO THE LEFT
L - Multiply the last terms in each set of parentheses FARTHEST TO THE RIGHT
I am joyous to assist you anytime.
which one? please help. Triangle ABC has the angle measures shown below.
measure of angle A is 20
step by step explaination:
sum of all three angles of a triangle = 180°
therefore angle s( A+B+C)= 180°
substitute the values of a, b and c angles
2x+5x+11x = 180
18x = 180
x= 180/18= 10 °
now check each given answers by putting the value of x, you will find only measure of 2x = 2x10= 20
The measurement of angle A will be equal to 20.
What is an angle?The angle is defined as the span between two intersecting lines or surfaces at or close to the point where they meet.
The sum of all three angles of a triangle = 180°
Therefore angle s( A+B+C)= 180°
substitute the values of a, b and c angles
2x + 5x + 11x = 180
18x = 180
x = 180 / 18 = 10 °
Now check each given answer by putting the value of x, you will find an only a measure of
2x = 2 x 10 = 20
Therefore the measurement of angle A will be equal to 20.
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Find the measure of the indicated arc
Answer:
m SQ = 95°
Step-by-step explanation:
The measure of the inscribed angle RSQ is one half the measure of its intercepted arc, that is
m RQ = 2 × 95° = 190°
To find the measure of SQ subtract the sum of the measures of SR and RQ from 360
m SQ = 360° - (75 + 190)° = 360° - 265° = 95°
3^8 a^10 b^-5 c^2 over 3^12 a^7 b^-3 c^-2 when a =4 b= 8 and c= 3
[tex]\bf \cfrac{3^8a^{10}b^{-5}c^2}{3^{12}a^7b^{-3}c^{-2}}\implies \cfrac{a^{10}a^{-7}c^2c^2}{3^{12}\cdot 3^{-8}b^{-3}b^5}\implies \cfrac{a^{10-7}c^{2+2}}{3^{12-8}b^{-3+5}}\implies \cfrac{a^3c^4}{3^4b^2}~\hfill \begin{cases} a=4\\ b=8\\ c=3 \end{cases}[/tex]
[tex]\bf \cfrac{4^3\cdot ~~\begin{matrix} 3^4 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{~~\begin{matrix} 3^4 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~\cdot 8^2}\implies \cfrac{~~\begin{matrix} 64 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{~~\begin{matrix} 64 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\implies 1[/tex]
Answer:
1Step-by-step explanation:
[tex]\dfrac{3^8a^{10}b^{-5}c^2}{3^{12}a^7b^{-3}c^{-2}}\qquad\text{use}\ \dfrac{x^n}{x^m}=x^{n-m}\\\\=3^{8-12}a^{10-7}b^{-5-(-3)}c^{2-(-2)}=3^{-4}a^3b^{-2}c^{4}\\\\\text{substitute:}\ a=4,\ b=8,\ c=3:\\\\(3^{-4})(4^3)(8^{-2})(3^4)=(3^{-4}\cdot3^4)\bigg(2^2\bigg)^3\bigg(2^3\bigg)^{-2}\\\\\text{use}\ (x^n)(x^m)=x^{n+m}\ \text{and}\ \bigg(x^n\bigg)^m=x^{nm}\\\\=(3^{-4+4})\bigg(2^{(2)(3)}\bigg)\bigg(2^{(3)(-2)}\bigg)=(3^{0})(2^6)(2^{-6})\\\\\text{use}\ x^{-n}=\dfrac{1}{x^n}\ \text{and}\ (x^n)(x^m)=x^{n+m}[/tex]
[tex]=(1)\left(2^{6+(-6)}\right)=2^0=1\\\\\text{Used}\ a^0=1\ \text{for any real value of}\ a,\ \text{except 0}.[/tex]
Can somebody please help me. I don’t understand it at all.
Step-by-step explanation:
Just pick a bunch of values of x, and use the formula to find the corresponding value of y.
For example
When x = 0, y = 0+5 = 5 ----> Plot the point (0,5) on graph paper
When x = 1, y = 1+5 = 6 ----> Plot the point (1,6) on graph paper
When x = 2, y = 2+5 = 7 ----> Plot the point (2,7) on graph paper
Then connect the dots to get a linear graph. You should get a graph that looks like the one attached.
You first make a table with x and y
like this: x | y
then you think of possible values for x then solve for y
it needs to be positive , 0, and a negative like:
under x, you do:
2
0
-3
then you take the equation and solve for y.
after, with the y values, create a Cartesian plane and plot the points
so the points would be (2,7), (0,5), and (-3,2)
then you connect the points and draw arrows on both ends.
then label the line w/ the equation
-------------------------------------------------------
hey btw, i learned this just yesterday. lol
great timing
Baking times at the cookie baking competition are normally distributed, with a mean time of 11 minutes and a standard deviation time of 2 minutes. Using the empirical rule, approximately what percent of cookies are finished between 7 and 15 minutes?
A) 32%
B) 68%
C) 95%
D) 99.7%
Answer:
C)95%
Step-by-step explanation:
According to the oxford math center,
"The Empirical Rule
The Empirical Rule gives us a rule of thumb for approximating the proportion of a Normal distribution that falls within 1, 2, or 3 standard deviations of its mean.
Also called the 68-95-99.7 rule in some texts, for what will soon be obvious reasons, the Empirical Rules states that approximately
68% of a Normal distribution can be found within 1 standard deviation of its mean
95% of a Normal distribution can be found within 2 standard deviations of its mean
99.7% of a Normal distribution can be found within 3 standard deviations of its mean
"
We find that the deviation time is 2 min.
Therefore, we use the information given by the oxford math center and gather that it is C, or, 95 percent.
Answer:
95%
Step-by-step explanation:
I'm taking the test
help please
1) Which of the following is not a line segment in the drawing?
2) Which of the following does not name the same line?
The option "KM" does not represent a direct line segment in the drawing as there is no straight path connecting points K and M without passing through another point.
The figure contains various labeled points connected by lines representing different segments except for NK; hence option NK does not name an existing line segment in the drawing.
1) In this case, all options refer to line segments except for "KM." The points K and M are not connected by a straight line; instead, point N lies between them. Therefore, KM is not a direct line segment in this drawing.
It's essential to understand that a line segment is named after its end points and consists of these points and all the points on the line between them. Since there is no direct path from point K to M without passing through another point (N), KM cannot be considered as a single, uninterrupted line segment.
2)The image you provided contains a geometrical diagram with five labeled points: J, K, L, M, and N. Line segments are drawn connecting these points forming an X shape. The options given are JL, MN, JK, and NK.
Upon careful examination of the image, it is evident that line segments JL (from point J to L), MN (from point M to N), and JK (from point J to K) are present in the drawing. However, NK (from point N to K) is not a line segment depicted in this drawing.
Use dimes, nickels, and pennies to show 42 cents. How many different ways can you show this amount?
Answer:
Step-by-step explanation:
You Can Use 4 dimes and 2 pennies
Or 42 Pennies, 8 Nickels and 2 pennies.
Hopefully this helps!
42 cents can be represented in a variety of ways using dimes (10 cents), nickels (5 cents), and pennies (1 cent). Some of the possible representations are 4 dimes and 2 pennies; 3 dimes, 2 nickels and 2 pennies; 8 nickels and 2 pennies, amongst others.
Explanation:The question is about displaying the number 42 cents using dimes, nickels, and pennies. Each dime is equal to 10 cents, nickel is 5 cents and penny is 1 cent. Here's a few methods:
4 dimes and 2 pennies3 dimes, 2 nickels, and 2 pennies8 nickels and 2 pennies2 dimes, 7 nickels, and 3 pennies1 dime, 6 nickels, and 7 pennies42 penniesIt's a fun exercise to see how many other ways you can come up with!
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what is the slope of the line shown below? (5, 11) (-5, -1)
Answer:
-6/-5 is the slope
Step-by-step explanation:
Y2 - Y1 / X2 - X1 so
-1 - 11 / -5 - 5 = -12 / -10 simply it and get -6 / -5
Slope equals rise over run
Answer:
6/5
Step-by-step explanation:
Find the value of x for which line a is parallel to line b. (21)
What is the measure of E, in degrees?
O A. 1550
O B. 1300
O
C. Cannot be determined
O
D. 125°
Answer:
B. 130
Step-by-step explanation:
Since both sides of the triangle are 10, given that angle D is 25. We can conclude that angle F is also 25.
Total angle of triangle is equal to 180.
angle D + angle F + angle E = 180
25 + 25 + E = 180
50 + E = 180
E = 180 - 50
angle E = 130
what is the soultion to 40(0.9-x)
Answer:
Step-by-step explanation:
(40*0.9)+(40*-x)
36-40X
Answer: 36-40X
Answer:
[tex]\displaystyle =36-40x[/tex]
Step-by-step explanation:
Distributive property:
↓
[tex]\displaystyle A(B+C)=AB+AC[/tex]
A= 40, B=0.9, and C=x
[tex]\displaystyle 40*0.9-40x[/tex]
Then multiply numbers from left to right.
[tex]40*0.9=36[/tex]
[tex]\displaystyle 36-40x[/tex], which is our answer.
When figures (including points) are rotated 270° counterclockwise about the origin, it is also the same rotating figures clockwise by what other degree amount? Please help!
The other degree amount is 90 in a clockwise rotation.
Select the correct answer.
A circle is described by the equation x2 + y2 + 14x + 2y + 14 = 0. What are the coordinates for the center of the circle and the length of the
A.
(-7, -1). 36 units
'B.
c.
D.
(7.1). 36 units
(7.1), 6 units
(-7, -1), 6 units
Next
Answer:
(- 7, - 1), 6 units
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - h)² = r²
where (h, k) are the coordinates of the centre and r is the radius.
Given
x² + y² + 14x + 2y + 14 = 0
Collect x/y terms together and subtract 14 from both sides
x² + 14x + y² + 2y = - 14
To obtain standard form use the method of completing the square
add ( half the coefficient of the x/y terms )² to both sides
x² + 2(7)x + 49 + y² + 2(1)y + 1 = - 14 + 49 + 1
(x + 7)² + (y + 1)² = 36 ← in standard form
with centre (- 7, - 1) and radius = [tex]\sqrt{36}[/tex] = 6
Tre determines the solution to the equation 3.57x + 1.61 = 4.71 - 2.63x is x = 0.5. He verifies his solution using the steps below.
Equation: 3.57x + 1.61 = 4.71 - 2.63x
Step 1: 3.57(0.5) + 1.61 = 4.71 - 2.63(0.5)
Step 2: 1.785 + 1.61 = 4.71 - 1.315
Step 3: 3.395 = 6.025
Which statement most accurately describes Tre’s error?
A. Tre made an error when determining the original solution of x = 0.5.
B. Tre made an error when substituting the solution in for x.
C. Tre made an error when multiplying each coefficient by 0.5.
D. Tre made an error when adding or subtracting.
Answer:
Option D. Tre made an error when adding or subtracting
Step-by-step explanation:
we have the equation
[tex]3.57x + 1.61 = 4.71 - 2.63x[/tex]
Solve for x
Group terms that contain the same variable and move the constant to the other side
[tex]6.2x= 4.71 - 1.61[/tex]
Combine like terms
[tex]6.2x=3.1[/tex]
[tex]x=0.5[/tex]
Verify
Step 1: 3.57(0.5) + 1.61 = 4.71 - 2.63(0.5) ---> is correct
Step 2: 1.785 + 1.61 = 4.71 - 1.315 ----> is correct
Step 3: 3.395 = 6.025 ---> is not correct
because
4.71-1.315=3.395 instead of 6.025
therefore
Tre made an error when subtracting
Answer: The answer is d
Step-by-step explanation:
What is the area of parallelogram ABCD?
____ square units
Answer:
13
Step-by-step explanation:
Here's a method of finding the area of any polygon knowing its vertices. I'm using this parallelogram as an example.
Make a table like this (each vertex with its x- and y-coordinates):
Pt x y
A 3 6
B 6 5
C 5 1
D 2 2
A 3 6
Now multiply each x-coordinate by the y-coordinate on the line below and write it on the right side. Bold type shows the first multiplication.
x y
A 3 6
B 6 5 15
C 5 1 6
D 2 2 10
A 3 6 12
Now multiply each y-coordinate by the x-coordinate on the line below and subtract from each produce you already have. Do each subtraction. Bold type shows the first multiplication.
x y
A 3 6
B 6 5 15 - 36 = -21
C 5 1 6 - 25 = -19
D 2 2 10 - 2 = 8
A 3 6 12 - 6 = 6
Add all the differences.
x y
A 3 6
B 6 5 15 - 36 = -21
C 5 1 6 - 25 = -19
D 2 2 10 - 2 = 8
A 3 6 12 - 6 = 6
+____
-26
The area of the polygon is the absolute value of half of the sum of the differences.
area = |-26/2| = |-13| = 13
You can calculate the area of a parallelogram using the formula: Area = base * height. To do this, you need the length of the base and the perpendicular height of the parallelogram. For example, if the parallelogram has a base of 5 units and a height of 3 units, its area will be 15 square units.
Explanation:The area of a parallelogram can be calculated with the formula: Area = base * height. In your question, you'll need to know the lengths of base and the height of the parallelogram ABCD to compute the area. It's essential to remember that the height is the perpendicular distance from the base to the top, not the length of the side.
Let's say, for example, the base of your parallelogram is 5 units and the height is 3 units. You would calculate the area as follows: Area = base * height = 5 units * 3 units = 15 square units.
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What is a great circle?
A. A circle on a sphere made by performing a plane cut anywhere on the sphere
B. A circle on a sphere that has the same radius and center as the sphere itself
C. A circle on a sphere that doesn't pass through the sphere's center
D. Another name for a sphere
Answer:
B
Step-by-step explanation:
It's not D. A sphere is a sphere. A billiard ball is a billiard ball. Both are spheres. No other name applies to the sphere.
It is not C. That might be true if you are talking about a circumference.
The exact definition is B. B is the answer.
A is not true. The cut must go through the center as B suggests.
use trigonometric identities cosec²X = 3cot X-1
Step-by-step explanation:
cosec²x = 1/sin²x = (sin²x+cos²x)/sin²x =1 + cos²x/sin²x = 1 + cot²x.
Therefore:
1+cot²x = 3cot x - 1
cot²x - 3 cot x + 2 = 0
let cot x = t
t²-3t+2=0
t²-2t-t+2=0
t(t-2)-(t-2)=0
(t-1)(t-2)=0
t1=1
t2=2
so:
cot x = 1 then x1 = π/4 + πk
cot x = 2 then x2 = arccot(2) + πk
k is an integral.
A rectangular prism has a base that is 5cm by 7cm and a height of 12cm if all dimensions are doubled what happens to the volume?
Answer:
The volume increased eightfold.Step-by-step explanation:
The formula of a volume of a rectangular prism:
[tex]V=lwh[/tex]
l - length
w - width
h - height
We have l = 5cm, w = 7cm and h = 12cm.
Substitute:
[tex]V=(5)(7)(12)=420\ cm^3[/tex]
Doubled the dimensions:
l' = (2)(5cm) = 10cm, w' = (2)(7cm) = 14cm, h = (2)(12cm) = 24cm.
Calculate the new volume:
[tex]V'=(10)(14)(24)=3360cm^3[/tex]
Calculate the quotient [tex]\dfrac{V'}{V}[/tex]
[tex]\dfrac{3360}{420}=8[/tex]
Generalization:
V = lwh - the volume of a prism l × w × h
2l × 2w × 2h - new dimensions
V' = (2l)(2w)(2h) = 8lwh = 8V - new volume
As Rainsford struggles in the water, the boat travels onward without him. Quickly, he retains his wits. Instead of panicking, he decides to head toward the sound of the gunshots. He does so _________ he realizes where there are gunshots, there are people. Hopefully, these people will be willing and able to help him.
Which transition best fills in the blank?
specifically
absolutely
because
later
Answer:
the answer is 'because'
Using the linear combaination method what is the solution to the system of linear equations 7x-2y=-20and9x+4y=-6
Answer:
x=-2 y=3
Step-by-step explanation:
7x-2y=-20
9x+4y=-6
Multiply the first equation by 2
2(7x-2y) = 2 * -20
14x - 4y = -20
Add this to the second equation
14x - 4y = -40
9x+4y=-6
--------------------------
23x = -46
Divide by 23
23x/23 = -46/23
x = -2
Now we solve for y
9x+4y=-6
9(-2) +4y = -6
-18 + 4y = -6
Add 18 to each side
-18+18 +4y = -6+18
4y = 12
Divide by 4
4y/4 = 12/4
y=3