The equations are x+y=50 and 7x + 12y = 450
x = the number of mirrors = 30
y = the number of pouches = 20
What is the solution to an equation?
In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.
Let x be the number of mirrors
Let y be the number of pouches
x+y=50......(1)
Each mirror is $7
cost of x mirrors = 7x
Each pouch is $12.
cost of y pouches = 12y
7x + 12y = 450 .........(2)
(1) => x=50-y ...........(3)
Substitute (3) into (2)
(2) => 7(50-y) + 12y = 450
350 - 7y + 12y = 450
5y = 450 - 350 = 100
y= 100/5 = 20
(1) => x = 50 - 20 = 30
Thus, x = the number of mirrors = 30
y = the number of pouches = 20
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HELP ASAP PLS
Simplify the expression.
negative 15 plus the quantity negative 3 and seven tenths plus 9 and 15 hundredths end quantity divided by 5 all times 3 squared minus 4 and 7 tenths
−13.16
−9.89
0.49
20.11
The value of the given expression is -6.93.
How can make the expression simpler?The question's expression is as follows:
minus 15 plus the amount negative 3 and 7 tenths + 9 and 15 hundredths at the end of the number divided by 5 times 3 squared less 4 and 7 tenths results in the answer.
Correctly reformat the expression
Thus, we have
-15 - 3.7 + 9.15/5 * 3^2 - 4.7
Calculate the exponent and quotient.
Thus, we have
-15 - 3.7 + 1.83 * 9 - 4.7
Consider the product
-15 - 3.7 + 16.47 - 4.7
Analyze the difference and the total.
-6.93
Consequently, -6.93 is the value of the supplied equation (none of the options is correct)
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What is an equation of the line that passes through the points (-8, 5) and (2, 0)?
Answer:
[tex]y=-\frac{1}{2}x+1[/tex]
Step-by-step explanation:
The slope of the line is [tex]\frac{5-0}{-8-2}=-\frac{1}{2}[/tex].
So, the equation is
[tex]y=-\frac{1}{2}(x-2) \\ \\ y=-\frac{1}{2}x+1[/tex]
WHAT IS STANDARD FORM for 3×1/10 +6× 1/100 + 8 x 1/1000
Answer:
3.456 × 108
Step-by-step explanation:
What is the amplitude of the graph of the
function f(x) = -5 cos (x + 2)-5?
Answer:
5
Step-by-step explanation:
The amplitude of the graph of a function of the form [tex]a\cos(bx+c)-d[/tex] is [tex]|a|[/tex].
Stefano owns a restaurant where his customers create their own pasta dishes. The customer chooses exactly one type of noodle, sauce, vegetable, and meat. The following table shows the options available to customers.
Create your own pasta
Noodle options Spaghetti, Penne, Linguine
Sauce options Tomato, Rosa, Alfredo
Vegetable options Mushroom, Onion, Green pepper, Tomato
Meat options Steak, Beef, Sausage, Chicken, Bacon
How many different pasta dishes can customers create
2
Select the correct answer from the drop-down menu.
A school administrator bought 6 desk sets. Each set consists of one table and one chair. He paid $48.50 for each chair. If he paid a total of $663
for the 6 sets, the cost of each table is
$
54.50
62.00
110.50
159.00
Let the function P be defined by P(x) = x³ + 2x² - 13x + 10. Mai divides P(x) by
x + 5 and gets:
x²-3x+2
x+5) x³ + 2x² - 13x + 10
−x3 – 5x2
-3x² - 13x
3x² + 15x
2x + 10
-2x - 10
0
How could we tell by looking at the
remainder that (x + 5) is a factor?
The roots of the equation are x1=1,x2=-5, and x3= 2.
What is the equation of root?Equation with quadratic roots. The quadratic equation's roots are the values of the variables that fulfill the equation. In other words, if f() = 0, then x = is the quadratic equation's root, f(x). Real roots of an equation f(x) = 0 are the x-coordinates of the places where the curve y = f(x) intersects the x-axis.
The equation x3+2x2-13x+10 has roots that you need to find.
x^3 + 2x^2 -13 x+10=0
In order to determine whether x=1 is a root for the equation, let's first start by substituting it:
1+2 -13 +10 =0
When one of the roots is x=1, a factor is (x-1)
We'll divide the function by the second component to determine it (x-1)
==> x^3 +2x^2-13x +10 =0
==> (x-1)(x^2+3x-10)=0
Consider factoring now:
==> (x-1)(x+5)(x-2)=0
==> x1=1,
x2=-5,
The roots of the equation are and x3= 2.
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NO LINKS!! Help me with the 2-Column Proof Part 2aa
Here is the two column proof:
Statement Reason
M is the midpoint of AB GivenAM = AB/2 Definition of midpointMB = AB/2 Definition of midpointAM = AB Transitive property of equalityProvedA club collected $3,472 to buy computers. if each computer costs $680, estimate the number of computers that the club can buy explan
This is how I need to answer it:
Answer: 5 computers
Step-by-step explanation:
You would take the total amount collected and divide it by the cost of a computer.
3472/680=5.10
Since the number is not a whole number you would round down since you can not buy part of a computer. Therefore, the club can only buy 5 computers.
Find the product of 320and 23
Answer:
7360
Step-by-step explanation:
(320 · 20) + (320 · 3)
6400 + 960
7360
1
Given F (0, 2) and G (2,6), if point S lies 1/3 of the way along FG, closer to F than to G, find the
coordinates of S. Leave your answer in fraction form.
The coordinates of S(x₁, y₁)=(3/2 , 5) if F(0, 2) and G(2,6) and the lines divided in the ratio 1:3
What is a section formula?Finding the ratio by which a line segment is divided by a point internally or externally in coordinate geometry is done using the Section formula. The centroid, incenter, and ex center of a triangle are determined using it. Finding systems' centers of mass, equilibrium locations, etc. are all done using this method in physics. Finding the ratio by which a line segment is divided by a point internally or externally in coordinate geometry is done using the Section formula. The centroid, incenter, and ex center of a triangle are determined using it.
Given,
F(0, 2) and G(2, 6)
And also given that the points S lies on the way along FG then:
The lines divides the ratio,
1:3= m:n
Here we have to find the coordinates of S, we get:
S(x₁, y₁)=((mx₁+n x₂)/(m+ n), (my₁+n y₂)/(m+ n))
=((1(0)+3(2))/4 , (1(2)+3(6))/4)
=(6/4 , 20/4)
=(3/2 , 5)
S(x₁, y₁)=(3/2 , 5)
Therefore, the coordinates of S(x₁, y₁)=(3/2 , 5).
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Divide the polynomials.
Your answer should be a polynomial.
x² - 36
x − 6
Answer:
the answer to the division problem is `1x + 6` (a polynomial).
Step-by-step explanation:
To divide polynomials, we use the long division method. Here's how we can divide x² - 36 by x - 6:
x² - 36 |
--------
x - 6
First, we divide the leading coefficient of the numerator (which is 1) by the leading coefficient of the denominator (which is 1).
We get 1 / 1 = 1 as the first coefficient of our quotient.
x² - 36 |
--------
x - 6
1
Then, we multiply the quotient by the denominator and subtract it from the numerator.
We get (1 * (x - 6)) = x - 6, and x² - 36 - (x - 6) = x² - x - 30.
x² - 36 |
--------
x - 6
1
x - 6
----------
x² - x - 30
We repeat the process, dividing the leading coefficient of the new numerator (which is 1) by the leading coefficient of the denominator (which is 1).
We get 1 / 1 = 1 as the next coefficient of our quotient.
x² - 36 |
--------
x - 6
1
x - 6
----------
x² - x - 30
1
We multiply the quotient by the denominator and subtract it from the numerator.
We get (1 * (x - 6)) = x - 6, and x² - x - 30 - (x - 6) = x² - 2x + 24.
x² - 36 |
--------
x - 6
1
x - 6
----------
x² - x - 30
1
x - 6
---------------
x² - 2x + 24
We repeat the process one more time, dividing the leading coefficient of the new numerator (which is 1) by the leading coefficient of the denominator (which is 1).
We get 1 / 1 = 1 as the next coefficient of our quotient.
x² - 36 |
--------
x - 6
1
x - 6
----------
x² - x - 30
1
x - 6
---------------
x² - 2x + 24
1
We multiply the quotient by the denominator and subtract it from the numerator.
We get (1 * (x - 6)) = x - 6, and x² - 2x + 24 - (x - 6) = x² - 3x + 18.
x² - 36 |
--------
x - 6
1
x - 6
----------
x² - x - 30
1
x - 6
---------------
x² - 2x + 24
1
x - 6
------------------
x² - 3x + 18
Since the degree of the new numerator is less than the degree of the denominator, we have found the complete quotient.
So, the quotient is `1x + 6`, and the remainder is `x² - 3x + 18`.
Therefore, the answer to the division problem is `1x + 6` (a polynomial).
Answer:
x + 6
Step-by-step explanation:
[tex]\frac{x^{2} -36}{x-6}[/tex]
[tex]\frac{(x+6)(x-6)}{x-6}[/tex]
x + 6
I will give Brainliest. 50 Point question when I give you Brainliest you will get 100 Points!
The equivalent expressions are:
1. C. 1/15x - 14y
2. B. 2x - 4 - 10x + 15
3. The expression we can use are:
64 + 64(0.015)
4. The expressions that represent the sale price are:
0.7p
p - 0.3p
(1 - 0.3)p
What are Equivalent Expressions?If the simplest form of two expressions have the same value, then they are equivalent expressions.
1. Simplify 2/5x - 3y - 1/5x - 11y by combining like terms to determine the expression that is equivalent to it:
2/5x - 1/5x - 3y - 11y
1/15x - 14y
The answer is: C. 1/15x - 14y
2. Simplify 2(x - 2) - 5(2x - 3), by first opening the parentheses:
2x - 4 - 10x + 15
The equivalent expression is: B. 2x - 4 - 10x + 15
3. The percentage error allowed is 1.5% = 1.5/100 = 0.015.
Therefore, the expression we can use are:
64 + 64(0.015)
4. 30% is, 30/100 = 0.3.
Original price = p = $100.
0.3 of $100 = 0.3(100) = $30
Sale price = 70% of original price = 0.7(100) = $70.
Therefore, the expressions of the sale price of the bicycle are:
0.7p
p - 0.3p
(1 - 0.3)p
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account c has a 3.9 % apr compounded daily ( 365 times per year). determine the account value's growth factor and percent change per compounding period.
Answer:
Step-by-step explanation:
The compound interest period rate is P = Po(1±r/t)n(t)
Here,
r = .039
t = 365
The daily rate in this situation is = .039/365
The factor for 1 compounding period for a year = (1+(.039/365))365 = 1.039768317
The growth factor is = 3.9768317%
The accounts value's growth factor is 1.0000107227, and the percent change per compounding period is 0.107227%.
What is the growth factor?
The account value's growth factor is the factor by which the account value increases each compounding period. It is given by the formula:
[tex]$growth factor$ = (1 + APR /{$compounding frequency$}) ^ {($compounding frequency$ / $period$)}[/tex]
In this case, the APR is 3.9%, the compounding frequency is 365 times per year (daily), and the period is one year. Plugging these values into the formula, we get:
growth factor = (1 + 0.039 / 365) ^ (365 / 1) = 1.0000107227
The percent change per compounding period is the amount by which the account value increases each compounding period, expressed as a percentage. It is given by the formula:
percent change = (growth factor - 1) * 100
Plugging the value of the growth factor that we calculated earlier into this formula, we get:
percent change = (1.0000107227 - 1) * 100 = 0.107227%
Therefore, the account value's growth factor is 1.0000107227, and the percent change per compounding period is 0.107227%.
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It takes 10 pounds of tomatoes to make 3 cups of tomato paste.
Type the answers in the boxes below.
1. At this rate, how many cups of tomato paste can be made with 25 pounds of tomatoes?
cups of tomato paste
2. At this rate, how many pounds of tomatoes are needed to make 14 cups of tomato paste?
pounds of tomatoes
7.5 cups of tomato paste can be made from 25 pounds and 14 cups can make 46.67 pounds.
What is unitary method?The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.
Given, it takes 10 pounds to make 3 cups of tomato paste.
Thus, with 1 pound, number of cups can be made is equal to (3/10) cups
Thus, using 25 pounds, number of cups can be made is equal to
(3/10)*25
= 7.5 cups
3 cups of tomato paste can be made from 10 pounds
1 cup of tomato paste can be made from (10/3) pounds
14 cups of tomato paste can be made from
(10/3)*14
= 46.67 pounds
Thus, 7.5 cups of tomato paste can be made from 25 pounds and 14 cups can make 46.67 pounds.
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Mrs. Saunders bought a 19 pound turkey for Thanksgiving. The total cost of the turkey was $25.65. What was the cost of turkey per pound? Write an equation to represent the situation
The cost of turkey per pound is $1.35 and the equation which represents the situation is 19x - 25.65 = 0.
What is the linear equation?
An algebraic equation of the form y=mx+b is referred to as a linear equation. m is the slope, and b is the y-intercept, and all that is involved is a constant and a first-order (linear) term. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."
We have,
19 turkey pound
$25.65
the cost of turkey per pound?
so,
25.65 / 19 = 1.35
the cost of turkey per pound is $1.35.
The equation becomes:
let's take x = $1.35
19x - 25.65 = 0
Hence, the cost of turkey per pound is $1.35 and the equation which represents the situation is 19x - 25.65 = 0.
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Write the parametric equations below as a Cartesian equation by eliminating the parameter.
x(t)=−8t
y(t)=−8t+1
The cartesian equation is y=x+1 for the parametric equations x(t)=−8t and
y(t)=−8t+1
What is Cartesian Equation?A cartesian equation for a curve is an equation in terms of x and y only
The two parametric equations are
x=-8t...(1)
y=-8t+1...(2)
Convert the second equation as below.
(1-y)/8=t
Now plug in t= (1-y)/8 in equation 1.
x=-8(1-y)/8=y-1
x=y-1 is one cartesian equation.
Now let us find the other cartesian equation
t=-x/8
Plug in t value in y.
y=-8(-x/8)+1
y=x+1
Hence the cartesian equation is y=x+1 for both parametric equations x(t)=−8t and y(t)=−8t+1
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As dry air moves upward, it expands. In so doing, it cools at a rate of about 1°C for every 100 m rise, up to about 12 km.
If the ground temperature is 18°C, write a formula for the temperature at height x km. T(x) =
What range of temperature will a plane be exposed to if it takes off and reaches a maximum height of 6 km?
Write answer in interval notation. The range is
The formula for the function T(x) is T(x) = 18 - x/100
The temperature at a height of 6 km is 17.94°CThe range in interval notation is (-oo, oo)The formula for the functionFrom the question, we have the following parameters that can be used in our computation:
Rate = 1°C for every 100 m rise
Ground temperature = 18°C
This means that the function can be represented as
T = Ground temperature (G) - Rate * Height (x)
Where
T is temperatureG is the temperature at ground level.x is the height above ground level measured in metersSo, we have
T(x) = 18 - x/100
The temperature at a height of 6 kmThis means that
x = 6
Recall that
T(x) = 18 - x/100
So, we have
T(6) = 18 - 6/100
Evaluate
T(6) = 17.94
The range in interval notationIn (a), we have
T(x) = 18 - x/100
This is a linear function
So, the range in interval notation is (-oo, oo)
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a teacher wants to estimate the mean time (in minutes) that students take to go from one classroom to the next. his research assistant uses the sample time of 33 students to report the confidence interval as [7.08, 8.92].a. Find the sample mean time used to compute the confidence interval. (Round intermediate calculations to 4 decimal places, "sample mean" to 2 decimal places.) Sample meanb. Determine the confidence level if the sample standard deviation used for the interval is 1.901. (Round intermediate calculations to 4 decimal places, "t" value to 3 decimal places, and final answer to the nearest whole number.) Confidence level %
The average amount of time pupils spend moving from one classroom to the next is something a teacher wishes to estimate.
What is interval?
His research assistant reports the confidence interval with four decimal places and the "sample mean" with two decimal places using the sample time of 33 pupils. the sample mean duration applied to the confidence interval computation. the final result to the nearest whole number, and the confidence level if the sample standard deviation used for the interval is three decimal places. Confidence interval% level. His research assistant reports the confidence interval using a sample size of 41 pupils. His research assistant reports the confidence using a sample of 38 students. the sample mean duration applied to the confidence interval computation. 90 percentile of the population proportion's confidence interval.
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Francine received a gift card to buy cell
phone apps. She says that the card’s value
is enough to buy any of the apps:
recipes-$9.50, W02 sports-$10.50, or
Remote desktop-$12.00. Let v be the dollar
value of the gift card. Write an inequality
that best describes the value of the gift
Card.
How many apps can Francine buy with the giftcard? Explain
The inequality that best describes the value of the gift card is v ≥ 12
What is inequality?
An inequality in mathematics depicts the connection between two values in an algebraic statement that are not equal. One of the two variables on the two sides of the inequality may be greater than, greater than or equal to, less than, or less than or equal to another value, according to inequality signals.
The inequality above states that the gift card, v could have $12 or possibly more on it because we know the most expensive app his gift card can buy is $12.
The inequality that best describes the value of the gift card is v ≥ 12
He can buy apps that are worth greater than or equal to $12
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90000000000000000x900000000000000
Answer: 8.1e+31
Step-by-step explanation:
y=−2x+4 (left parenthesis ,-2)
The equation y = 2x + 4 has the following missing value: 3.
What is an equation's solution?The x and y values of an ordered pair whose values, if substituted into the equation, would make it true are the answer to the given equation.
According to the Given information
If the value of x is the missing value in the solution to the equation y = -2x + 4, and the solution is (x, -2) Hence, by adding y = -2 to the equation and solving for x, the value of x can be found:
-2 = -2x + 4
Take 4 away from both sides.
-2 - 4 = -2x + 4 - 4 (subtraction property of equality)
-6 = -2x
Add -2 to both sides.
-6/-2 = -2x/-2
3 = x
x = 3
The equation y = 2x + 4 has the following missing value: 3.
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A theater group made appearances in two cities. The hotel charge before tax in the second city was $1500 lower than in the first. The tax in the first city was 9.5% , and the tax in the second city was 10% . The total hotel tax paid for the two cities was 971.25
. How much was the hotel charge in each city before tax?
Answer: Let x = the charge in 1st city before taxes
Let y = the charge in 2nd city before taxes
Set up equation before taxes.
y = x - 1500 eq1
Set up equation for total tax paid.
0.065x + 0.06y = 378.75 eq2
Substitute eq1 into eq2.
0.065x + 0.06(x - 1500) = 378.75
0.065x + 0.06x - 90 = 378.75
0.125x - 90 = 378.75
0.125x = 468.75
x = 3750
Substitute this value of x into eq1.
y = 3750 - 1500
y = 2250
The hotel charge in city one is $3750 and the hotel charge in city two is $2250.
Step-by-step explanation:
The perimeter of a rectangle is 40 inches. Find the length and width if the length is an integer and the width is 2 times the next consecutive integer. Length = Width =
The values are;
Length = 6 inches
Width = 14 inches
How to determine the valuesThe formula for determining the perimeter of a rectangle is expressed as
P = 2( l + w)
Where;
P is the perimeterl is the lengthw is the widthFrom the information given, we have;
Length = x
Width = 2(x + 1) = 2x + 2
Now, substitute the values
40 = 2( x + 2x + 2)
expand the bracket
40 = 2(3x + 2)
40 = 6x + 4
collect like terms
6x = 40 - 4
6x = 36
x = 36/6
Divide the values
x = 6 inches
Length = 6 inches
Width = 2( 6 + 1) = 2(7) = 14 inches
Hence, the values are 6 and 14 inches
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The values are;
Length = 6 inches
Width = 14 inches
How to determine the values
The formula for determining the perimeter of a rectangle is expressed as
P = 2( l + w)
Where;
P is the perimeter
l is the length
w is the width
From the information given, we have;
Length = x
Width = 2(x + 1) = 2x + 2
Now, substitute the values
40 = 2( x + 2x + 2)
expand the bracket
40 = 2(3x + 2)
40 = 6x + 4
collect like terms
6x = 40 - 4
6x = 36
x = 36/6
Divide the values
x = 6 inches
Length = 6 inches
Width = 2( 6 + 1) = 2(7) = 14 inches
Hence, the values are 6 and 14 inches
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Help pls this should be easy someone pls
Answer: the second one
Please help me this is due today
Answer:
x=20
Step-by-step explanation:
both of these angles equal each other
3x+50=6x-10
-3x. -3x
50= 3x-10
+10 +10
60=3x
/3. /3
20=x
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1cm:10mm into a scale factor
One centimeter is equivalent to 10 millimeters.
Converting the cm to mm
10mm:10mm
The scale factor is 1:1 because the two are equal
Hope this helps :)
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- Jeron
Evaluate the expression for w=-5
2 w²-3(-9 w-40)²=
Submit
Answer: 25
Step-by-step explanation:
simplify (z⁹z-3)-2
Please
Answer: [tex]z^{10}[/tex]-5
Step-by-step explanation:
Represent the following sentence as an algebraic expression, where "a number" is the
letter x. You do not need to simplify.
5 is subtracted from the product of 3 and a number.
Answer:
3x -5
Step-by-step explanation:
You want the algebraic expression for "5 is subtracted from the product of 3 and a number".
Product"The product of 3 and a number" is represented by 3x.
SubtractionSubtraction is indicated by a minus sign. When 5 is subtracted from the product, the expression is written ...
3x -5