Given
[tex]\begin{gathered} 7(4x+1)-3x=5x-13 \\ 28x+7-3x=5x-13 \\ 25x-5x=-13-7 \\ 20x=-20 \\ x=-1 \end{gathered}[/tex]5. There are 9.75 ounces of Cinnamon Toast Crunch in a bowl. Additional cereal ispoured into the bowl at a rate of 1.5 ounces per second. How many ounces are inthe bowl after 3 seconds?
Question:
There are 9.75 ounces of Cinnamon Toast Crunch in a bowl. Additional cereal is poured into the bowl at a rate of 1.5 ounces per second. How many ounces are in the bowl after 3 seconds?
Solution:
If additional cereal is poured into the bowl at a rate of 1.5 ounces per second, then in 3 seconds the additional cereal into the bowl is 1.5x 3 = 4.5 ounces. Thus after 3 seconds, the bowl has the original amount that it already had and the new aggregate:
9.75 ounces + 4.5 ounces = 14.25
then, the correct answer is:
14.25
A business woman buys a new computer for $4000. for each year that she uses it the value goes depreciates by $400 the equation below gives the value y of the computer after x years. What does the x intercept mean in this situation? Find the x intercept. After how many years will the value of the computer be $2000Y=-400x+4000
Step 1: Write the equation
y = -400x + 4000
Step 2:
The intercept in the equation represents time in years.
x-intercept represents the total length of time taken in years for the computer to values to depreciate to $0.
step 3: Find the x-intercept
To find the x-intercept, you will have to find the time taken for the computer value to depreciate to $0.
y = $0
[tex]\begin{gathered} \text{From the equation.} \\ y\text{ = -400x + 4000} \\ 0\text{ = -400x + 4000} \\ 400x\text{ = 4000} \\ x\text{ = }\frac{4000}{400} \\ x\text{ = 10} \end{gathered}[/tex]The x-intercept = 10 years
Step 4:
To find the number of years take for the computer value to depreciate to $2000.
You will substitute the value of y = $2000 and find the value of x.
Therefore
[tex]\begin{gathered} y\text{ = -400x + 4000} \\ 2000\text{ = -400x + 4000} \\ 400x\text{ = 4000 - 2000} \\ 400x\text{ = 2000} \\ x\text{ = }\frac{2000}{400} \\ \text{x = 5 years} \end{gathered}[/tex]It will take 5 years for the value of the computer to depreciate to $2000.
Question number 3: which of the following is equal to 18x*7 y*6?
Solution:
Given:
[tex]\sqrt{18x^7y^6}[/tex]Splitting the expressions further to get the perfect squares out:
[tex]\begin{gathered} \sqrt{18x^7y^6}=\sqrt{9\times2\times(x^6\cdot x)\times(y^3)^2} \\ =\sqrt{9\times2\times(x^3)^2\cdot x\times(y^3)^2} \end{gathered}[/tex][tex]\begin{gathered} \sqrt{18x^7y^6}=\sqrt{9\times2\times(x^3)^2\cdot x\times(y^3)^2} \\ =3x^3y^3\sqrt{2x} \end{gathered}[/tex]Therefore, the correct answer is:
[tex]3x^3y^3\sqrt{2x}[/tex]The revenue function R in terms of the number of units sold, a, is given as R = 300x - 0.4x^2where R is the total revenue in dollars. Find the number of units sold a that produces a maximum revenue?Your answer is x =What is the maximum revenue?
1) Considering the Revenue function in the standard form:
[tex]R(x)=-0.4x^2+300x[/tex]2) Since this is a quadratic function, we can write out the Vertex of this function:
[tex]\begin{gathered} x=h=-\frac{b}{2a}=\frac{-300}{2(-0.4)}=375 \\ k=f(375)=-0.4(375)^2+300(375)\Rightarrow k=56250 \end{gathered}[/tex]3) So, we can answer this way:
[tex]x=375\:units\:yield\:\$56,250[/tex]What value of t makes the following equation true?
5t−2=6t−7
Which subsets of numbers does belong to?
Natural numbers are just counting numbers. It doesn't include a negative number. Integers include both positive and negative whole numbers. rational numbers are fractions that can be expressed as two integers. We can have - 8/1 = - 8
Finally, real numbers is any positive or negative number. It includes integers and rational numbers. Therefore, the subset that contains - 8 would be
real, rational and integer numbers
I NEED HELP
5C/2 = 20
you would have to do this backwards
20 times 2 would remove the /2
5c=40
40 divided by 5
is
8
C=8
Expand the following using the suitable identity.(-x + 2y - 3z)^2
Given the expression (-x + 2y - 3z)², we are to expand it using a suitable identity.
Using the square of the sum of trinomial identity expressed as:
[tex](a+b+c)^2=a^2+b^2+c^2+2\text{ab+2ac+2bc}[/tex]From the given expression;
[tex]\begin{gathered} a=-x \\ b=2y \\ c=-3z \end{gathered}[/tex]Substitute the parameters into the identity to expand as shown:
[tex](-x+2y-3z)^2=(-x)^2+(2y)^2+(-3z)^2+2(-x)(2y)+2(-x)(-3z)_{}+2(2y)(-3z)[/tex]
Simplify the result to have:
[tex](-x+2y-3z)^2=x^2+4y^2+9z^2-4xy+6xz_{}-12yz[/tex]This gives the correct expansion using a suitable identity
Which postulate or theorem could you use to prove (triangle)XYZ = (triangle)ABC?Choose the correct answer below.AAS theoremSSS postulateASA postulateSAS postulate
From the given figures in the 2 triangles XYZ and ABC
mXZ = AC
m
Since we have two equal angles and the sides between them are equal, then
The 2 triangles are congruent using ASA postulate
The answer is C
69=2g-24 I NEED TO FIND G
Benjamin mows two lawns. The first lawn is 8 meters long and 7 meters wide. The second lawn has the same length, and a width that is 6 times as much as the first one. What is the total area of the two lawns?
Area overall is 392 square metres. The two lawns' combined area is therefore 392 square metres.
what is square ?A square is a quadrilateral in geometry that has four equal sides and four right angles (90-degree angles). It is a unique kind of both a rhombus and a rectangle. A square is made up of four equal-length sides, two equal-length diagonals, and right-angle diagonal cuts. A square's area and perimeter can be calculated by multiplying one of its sides by itself (squared), and one of its sides by four, respectively. Because of their symmetry and regularity, squares are frequently employed in mathematics and building.
given
By multiplying the first lawn's length by its breadth, one may determine its area: 56 square metres is the size of the first lawn, which is 8 metres by 7 metres.
The second lawn's breadth is six times that of the first lawn's, so:
The second lawn's width is equal to 6 × 7 metres, or 42 metres.
The second lawn is the same length as the first one, so:
The second lawn is 8 metres long.
The second lawn's area is calculated by multiplying its length by its width:
The second lawn is 336 square metres in size (8 metres by 42 metres).
The first and second lawns' combined areas make up the overall area of the two lawns:
Total area equals the sum of the first and second lawns.
56 square metres + 336 square metres make up the total area.
Area overall is 392 square metres. The two lawns' combined area is therefore 392 square metres.
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Find the measure of the arc or central angle indicated. Assume that lines which appear to bediameters are actual diameters.
From the given circle, the measure of the arc or the central angle indicated is as shown at the center of the circle is subtended by the arc
Hence, the measure of the arc or central angle indicated is 65° ,Option B
An empty rectangular tank measures 60 cm by 50 cm by 56 cm. It is being filled with water flowing from a tap at rate of 8 liters per minute. (a) Find the capacity of the tank (b) How long will it take to fill up (1 liter = 1000 cm
(a) The capacity of the tank is its volume, which we can calculate by multipling its sides:
[tex]V=abc=60\cdot50\cdot56=168000[/tex]This is, 168000 cm³. It is equivalent to 168 L.
(b) If the tank is being filled at a rate of 8 liters per minute, we can find the time to fill ir by dividing its capacity by the rate:
[tex]t=\frac{168}{8}=21[/tex]That is, it will take 21 minutos to fill it up.
The points (-6, -10) and (23, 6) form a line segment.
Write down the midpoint of the line segment.
A line segment has the endpoints at (-6, -10) and (23, 6) then the midpoints of the line segment will be (17, -2).
What is meant by line segment?An area or portion of a line with two endpoints is called a line segment. A line segment, in contrast to a line, has a known length. A line segment's length can be estimated by utilizing either metric measurements like millimeters or centimeters, or conventional measurements like feet or inches.
A line segment has the endpoints at (-6, -10) and (23, 6).
Mid point of the line segment is given by [tex]$\left(\frac{x_1+x_2}{2}\right),\left(\frac{y_1+y_2}{2}\right)$[/tex]
The midpoints of the line segment will be
= [tex]$\frac{23+-6}{2}[/tex], [tex]$\frac{-10+6}{2}}[/tex]
= 17, -2
Therefore midpoints of the line segment will be (17, -2).
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Together, Katya and Mimi have 480 pennies in their piggy banks. After Katya loses 1/2 of her pennies and Mimi loses 2/3 of her pennies, they have an equal number of pennies left. How many pennies did they lose altogether?
The number of pennies they lose altogether is 288 pennies.
How to find the number of pennies they lost together?Together, Katya and Mimi have 480 pennies in their piggy banks.
Therefore, there total amount of pennies is 480.
After Katya loses 1/2 of her pennies and Mimi loses 2/3 of her pennies, they have an equal number of pennies left.
Therefore,
let
x = number of pennies Katya have
y = number of pennies Mimi have
Hence,
x + y = 480
x = 480
Katya pennies left = x - 1 / 2x = 1 / 2x
Mimi pennies left = y - 2 / 3 y = 1 / 3 y
1 / 2 x = 1 / 3 y
2y = 3x
y = 3 / 2 x
Substitute the value in equation(i)
x + 3 / 2 x = 480
2.5x = 480
x = 480 / 2.5
x = 192
Therefore,
192 + y = 480
y = 480 - 192
y = 288
The number of pennies they loose can be calculated as follows;
Katya losses = 1 / 2 × 192 = 96Mimi losses = 2 / 3 × 288 = 192Therefore, they lost 96 + 192 = 288 pennies altogether.
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How do I find the linear equation for this? (y=mx+b)
Okay, here we have this:
Considering the provided table, we are going to find the corresponding linear equation, so we obtain the following:
To do this we will start using the information in the slope formula, then we have:
m=(y2-y1)/(x2-x1)
m=(190-(-30))/(19-9)
m=220/10
m=22
Now, let's find the y-intercept (b) using the point (9, -30):
y=mx+b
-30=(22)9+b
-30=198+b
b=-30-198
b=-228
Finally we obtain that the linear equation is y=22x-228
Answer:
Step-by-step explanation:
These are the two methods to finding the equation of a line when given a point and the slope: Substitution method = plug in the slope and the (x, y) point values into y = mx + b, then solve for b. Use the m given in the problem, and the b that was just solved for, to create the equation y = mx + b.
distance between (11,-5) and (0,1)
Here,point can be written as:
[tex]\begin{gathered} x1=11, \\ y1=-5 \\ x2=0 \\ y2=1 \end{gathered}[/tex]The formula for the distance between the points as follows;
[tex]\begin{gathered} d=\sqrt{(x1-x2)^2+(y1-y2)^2} \\ d=\sqrt{(11-0)^2+(-5-1)^2} \\ d=\sqrt{121+36} \\ d=\sqrt{157} \\ d=12.53 \end{gathered}[/tex]Thus, the distance between the point is 12.53.
Let log, A = 3; log, C = 2; log, D=5 D? what is the value of
Evaluate the value of expression.
[tex]\begin{gathered} \log _b\frac{D^2}{C^3A}=\log _bD^2-\log _bC^3-\log _bA \\ =2\log _bD-3\log _bC-\log _bA \\ =2\cdot5-3\cdot2-3 \\ =10-6-3 \\ =1 \end{gathered}[/tex]So answer is 1.
Mr. Bensoua buys 3 bags of Flaming Hot Cheetos for every 4 bags of Takis. He buys a total of 14 bags of chips. If the Flamin Hot Cheetos cost $2 per bag and the Takis cost $2.50 per bag, how much did Mr. Bensoua spend on all of the chips
Statement Problem: Mr. Bensoua buys 3 bags of Flaming Hot Cheetos for every 4 bags of Takis. He buys a total of 14 bags of chips. If the Flamin Hot Cheetos cost $2 per bag and the Takis cost $2.50 per bag, how much did Mr. Bensoua spend on all of the chips?
Solution:
When Mr. Bensoua buys 4 bags of Takis, he buys 3 bags of Flaming Hot Cheetos.
When he buys another 4 bags of Takis, he buys 3 bags of Flaming Hot Cheetos.
At the end, he buys 8 bags of Takis and 6 bags of Flaming Hot Cheetos and that makes it a total of 14 bags of chips.
The cost of Takis per bag is $2.50, the cost of 8 bags of Takis is;
[tex]\text{2}.50\times8=20[/tex]The cost of Flaming Hot Cheetos per bag is $2., the cost of 6 bags of Takis is;
[tex]2\times6=12[/tex]Hence, the total amount Mr. Bensoua spends is;
[tex]20+12=32[/tex]CORRECT ANSWER: $32
what does frilling mean
Answer:
A ruffled, gathered, or pleated border or projection, such as a fabric edge used to trim clothing.
Step-by-step explanation:
Brainlest, Please!
There are four Defenders on a soccer team if this represents 20% of the players on the team which equation can be used to find the total number of players on the team
Given in the question:
a.) There are four Defenders on a soccer team.
b.) This represents 20% of the players on the team.
Use the graph of y = f (x) to find the following value of f. f(2) =
Answer:
f(2)=4
Explanation:
Consider the graph below:
When x=2, the value of f(x) = 4 (the poiny circled in blue above).
Therefore:
[tex]f(2)=4[/tex]The value of f(2) is 4.
Given right triangle ABC, with altitude CD intersecting AB at point D. If AD = 5 and DB = 8, find the length of CD, in simplest radical form. In your video include whether you would use SAAS or HYLLS to solve (and WHY), the proportion you would set up, how you would solve for the missing side, and how you know your answer is in simplest radical form.
First we dra a triangle:
To prove that the triangles are similar we have to do the following:
Considet triangles ABC and ACD, in this case we notice that angles ACB and ADC are equal to 90°, hence they are congruent. Furthermore angles CAD and CAB are also congruent, this means that the remaining angle in both triangles will also be congruent, therefore by the AA postulate for similarity we conclude that:
[tex]\Delta ABC\approx\Delta ACD[/tex]Now consider triangles ABC and BCD, in this case we notice that angles ACB and BDC are congruent since they are both equal to 90°. Furthermore angles ABC and DBC are also congruent, this means that the remaining angle in both triangles will, once again, be congruent. Hence by the AA postulate we conclude that:
[tex]\Delta ABC\approx\Delta BCD[/tex]With this we conclude that traingles BCD and ACD are both similar to triangle ABC, and by the transitivity property of similarity we conclude that:
[tex]\Delta ACD\approx BCD[/tex]Now that we know that both triangles are similar we can use the following proportion:
[tex]\frac{h}{x}=\frac{y}{h}[/tex]this comes from the fact that the ratios should be the same in similar triangles.
From this equation we can find h:
[tex]\begin{gathered} \frac{h}{x}=\frac{y}{h} \\ h^2=xy \\ h=\sqrt[]{xy} \end{gathered}[/tex]Plugging the values we have for x and y we have that h (that is the segment CD) has length:
[tex]\begin{gathered} h=\sqrt[]{8\cdot5} \\ =\sqrt[]{40} \\ =\sqrt[]{4\cdot10} \\ =2\sqrt[]{10} \end{gathered}[/tex]Therefore, the length of segment CD is:
[tex]CD=2\sqrt[]{10}[/tex]help meeeeeeeeee pleaseee !!!!!
The composition will be:
(g o h)(x) = 5*√x
By evaluating in x = 0, we get:
(g o h)(0) = 0
How to evaluate the composition?Here we have the two functions:
g(x) = 5x
h(x) = √x
And we want to get the composition:
(g o h)(x) = g( h(x))
So we need to evaluate g(x) in h(x), we will get:
g( h(x)) = 5*h(x) = 5*√x
And now we want to evaluate this in x = 0, we will et:
(g o h)(0) = 5*√0 = 0
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What is the mean and median of the data set
The mean of a data set is the sum of the data divided by the total number of data.
The median of a data set is the middle number in the set (after the numbers have been arranged from least to greatest, or, if there is an even number of data, the median is the average of the two middle numbers.
You have the next data set:
[tex]\begin{gathered} \lbrace11,11,11,11,12,12,12,13,13,13,13,13,13,14,15,15,15,15,15, \\ 15,16,16,16,16,16,17,17,17\rbrace \end{gathered}[/tex]A total of 28 data.
The mean is equal to the sum of the 28 numbers and then divided into 28:
[tex]undefined[/tex]given: S is the midpoint of BT ; BO || AT prove:
"S is the midpoint of BT": this is given.
BO || AT: this is given.
SB = ST: definition of midpoint.
alternate interior
vertical
ΔBOS = ΔTAS: SAS or ASA (both are right).
Pour subtracted from the product of 10 and a number is at most-20,
we have
four subtracted from the product of 10 and a number is at most-20
Let
n ----> the number
so
[tex]10n-4\leq-20[/tex]solve for n
[tex]\begin{gathered} 10n\leq-20+4 \\ 10n\leq-16 \\ n\leq-1.6 \end{gathered}[/tex]the solution for n is the interval (-infinite, -1.6]
All real numbers less than or equal to negative 1.6
write 0.751 as a percentage
To convert decimal numbers to percentage, what we need to do is to multiply the decimal number by 100, and we will get the representation as a percentage.
In this case we have the decimal number:
[tex]0.751[/tex]We multiply that number by 100 to write is as a percentage:
[tex]0.751\times100=71.5[/tex]Answer: 75.1%
Choose the best description of its solution. If applicable, give the solution.
Given:
[tex]\begin{gathered} -x-3y=-6\ldots\text{ (1)} \\ x+3y=6\ldots\text{ (2)} \end{gathered}[/tex]Adding equation(1) and equation(2)
[tex]\begin{gathered} -x-3y+x+3y=-6+6 \\ 0=0 \end{gathered}[/tex]The system has infinitely many solution .
They must satisfy the equation:
[tex]y=\frac{6-x}{3}[/tex]20. Two teachers measured the shoe size of each of their students. The datawere used to create the box plots shown.Mrs. Norris's Class567891011121314Shoe SizeMrs. Ganger's Class5 6+87111213149 10Shoe SizeBased on the data, which statement about the results must be true?The average shoe size is the same for both classes.The shoe sizes 6 and 13 are outliers for both classes.© Mrs. Norris's class and Mrs. Ganger's class have the sameinterquartile range.© The median shoe size for Mrs. Norris's class is greater than forMrs. Ganger's class.
The correct answer is the last sentence.
"The median shoe size for Mrs. Norris's class is greater than for
Mrs. Ganger's class".
