a =20, b =15, c= 60
1) Writing this we have
1st evening: a
2nd evening: b
3rd evening: c
a +b+ c = 85
b=5 -a
c=4a
2) So rewriting this out as an expression we have:
a + b+ c = 85 Plug into that in terms of "a"
a + 5-a + 4a = 85 Combine like terms
4a +5 = 85 subtract 5 from both sides
4a = 80 Divide both sides by 4
a = 20
2.2) Plug into each formula:
b =a -5
b = 20 -5
b = 15
20+15 + c = 85 Add them up
35 +c = 85 Subtract 35 from both sides
c = 85 -35
c= 60
Or we could have done it:
c = 4b
c= 4* 15
c= 60
3) Hence, the answer is a =20, b =15, c= 60
The pH of a fruit juice is 5.3 Find the hydronium ion concentration [H3O+] of the juice. Use the formula pH = -log[H30+]
Answer:
[tex]\lbrack H_3O^+\rbrack\text{ = }5.0\text{ }\times10^{-6\text{ }}moles\text{ per liter}[/tex]Explanation:
By definition, the pH of a solution is the negative logarithm to base 10 of the concentration of Hydroxonium or oxonium ion
Mathematically, we have this as:
[tex]pH=-log\lbrack H_3O^+\rbrack_{}[/tex]We can change the formula subject so we would have hydroxonium ion on the left
Mathematically, we have this as:
[tex]\lbrack H_3O^+\rbrack\text{ = ANTILOG (-pH)}[/tex]Finally, we have the calculation as follows:
[tex]\lbrack H_3O^+\rbrack\text{ = antilog(-5.3) = }0.000005011872[/tex]In the scientific form,we have this as:
[tex]5.0\text{ }\times10^{-6\text{ }}moles\text{ per liter}[/tex]
Question 1 of 10 The graphs below have the same shape. What is the equation of the red graph? w GE? F%= 3 - 74 G(X)
The equation of the red graph (Parabola) is g(x) = 1 – x².
The given graph is the graph of the parabolas.
We are given;
The equation of the blue graph (Parabola) is f(x) = 4 – x².
We need to find the equation of the red graph g(x).
Let's observe the graph;
All of the lines in the blue graph pass through point 4 on the graph. The same is true for the red line, except that they all pass through 1. As a result, we should alter the 4 in the blue line equation to a 1 to represent the red line.
The equation of the blue graph is:
f(x) = 4 – x²
Substitute 4 by 1;
p(x) = 1 – x² = g(x)
This is our required equation.
Thus, the equation of the red graph (Parabola) is g(x) = 1 – x².
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4. The triangles below lie on the same line. Find thehorizontal distance of the smaller triangle.25DA10Distance:pe here to searchN
Thus the horizontal distance of the smaller triangle is 2.
A quadratic function and an exponential function are graphed below. How do the decay rates of the functions compareover the interval -2
To check the decay rate, we need to check the variation in y-axis.
Since our interval is
[tex]-2We need to evaluate both function at those limits.At x = -2, we have a value of 4 for both of them, at x = 0 we have 1 for the exponential function and 0 to the quadratic function. Let's call the exponential f(x), and the quadratic g(x).
[tex]\begin{gathered} f(-2)=g(-2)=4 \\ f(0)=1 \\ g(0)=0 \end{gathered}[/tex]To compare the decay rates we need to check the variation on the y-axis of both functions.
[tex]\begin{gathered} \Delta y_1=f(-2)-f(0)=4-1=3 \\ \Delta y_2=g(-2)-g(0)=4-0=4 \end{gathered}[/tex]Now, we calculate their ratio to find how they compare:
[tex]\frac{\Delta y_1}{\Delta y_2}=\frac{3}{4}[/tex]This tell us that the exponential function decays at three-fourths the rate of the quadratic function.
And this is the fourth option.
• if the area of a square is 100cm ^2, what is the perimeter? • if the perimeter of a square is 116cm, what is it's area?
1) Given data:
Area of square = 100 cm square
[tex]A=a^2[/tex][tex]\begin{gathered} a^2=100 \\ a=10\operatorname{cm} \end{gathered}[/tex]The perimeter of square is,
[tex]\begin{gathered} P=4a \\ P=4\times10 \\ P=40\operatorname{cm} \end{gathered}[/tex]2) Given data:
Perimeter of square = 116 cm
[tex]P=4a[/tex][tex]\begin{gathered} 4a=116 \\ a=29 \end{gathered}[/tex]The area os square is,
[tex]\begin{gathered} A=a^2 \\ A=29\times29 \\ A=841\operatorname{cm}\text{ square} \end{gathered}[/tex]Solve for y. d = 5x + 5y 0 y = 5x-d 5 d-5.2 O Y = y = 5(d - 5x) o y Y d-5x 5
Given the equation:
[tex]d=5x+5y[/tex]Solve for y , which mean make y alone on the left side.
So,
[tex]5y=d-5x[/tex]Divide the equation by 5
[tex]y=\frac{d-5x}{5}[/tex]The answer is the last option
A club that has 20 members is selecting a 5 representatives to send to a national conference. How many different groups of 5 can there be?
There can be a total of 15504 groups of selection
How to determine the groups of selection?From the question, we have
Total number of persons, n = 20
Numbers to selection, r = 5 i.e. the committee members
The number of ways of selection could be drawn is calculated using the following combination formula
Total = ⁿCᵣ
Where
n = 20 and r = 5
Substitute the known values in the above equation
Total = ²⁰C₅
Apply the combination formula
ⁿCᵣ = n!/(n - r)!r!
So, we have
Total = 20!/15!5!
Evaluate
Total = 15504
Hence, the number of ways is 15504
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Answer:
There can be 4 groups of 5.
i forgot how i solved this, what im getting is 4x -24 which is wrong
Answer:
[tex](4x^2+22x-12)cm^2[/tex]Explanation:
From the given figure:
• The base of the triangle, b = (4x-2) cm
,• The perpendicular height, h = (2x+12) cm
The area of a triangle is calculated using the formula:
[tex]A=\frac{1}{2}bh[/tex]Substitute the given expressions:
[tex]\begin{gathered} A=\frac{1}{2}(4x-2)(2x+12) \\ Factor\text{ }4x-2\implies4x-2=2(2x-1) \\ A=\frac{1}{2}\times2(2x-1)(2x+12) \\ A=(2x-1)(2x+12) \end{gathered}[/tex]Next, open the brackets:
[tex]\begin{gathered} A=2x(2x+12)-1(2x+12) \\ =4x^2+24x-2x-12 \\ =(4x^2+22x-12)cm^2 \end{gathered}[/tex]The area of the triangle is:
[tex](4x^2+22x-12)cm^2[/tex]PLEASE HELP ME ASAP PLEASE PLEASE PLEASE
jaren is selling lampshades at a craft fair. for the price per lampshade in dollars is f (x) and it is a function of the
Number of lampshades bought as shown by the graph below. What is the total cost of buying 10 lampshades from Janet's stall
According to the graphic the total cost of buying 10 lampshades is 8 dollars
Marked angle 3 different ways
Answer:
where are question I don't understand this question
A piece of wire 5/4 m long is to be cut into 20 pieces of the same length. What is the length of each piece?Each piece is ____ m long.(Simplify your answer. Type an integer or a fraction.)
When we divide a fraction by a number, that's equivalent to multiplying the first fraction by the inverse of that number.
In this problem, we need to divide the fraction 5/4 by 20. So we obtain:
[tex]\frac{5}{4}\colon20=\frac{5}{4}\cdot\frac{1}{20}[/tex]Now, we need to multiply the numerator of the first fraction by the numerator of the second one, and the denominator of the first fraction by the denominators of the second one:
[tex]\frac{5}{4}\cdot\frac{1}{20}=\frac{5\cdot1}{4\cdot20}=\frac{5}{80}[/tex]Now, we need to simplify the answer. To do so, we can divide both the numerator and the denominator by 5:
[tex]\frac{5\colon5}{80\colon5}=\frac{1}{16}[/tex]Therefore:
Each piece is 1/16 m long.
The radius of a circle is 2 meters. What is the circle's circumference?r=2 mUse 3.14 for л.meters
To solve this problem, we will use the following formula for the circumference of a circle:
[tex]C=2\pi r,[/tex]where r is the radius of the circle.
Substituting
[tex]\begin{gathered} r=\text{ 2 m, } \\ \pi=3.14 \end{gathered}[/tex]in the above formula, we get:
[tex]C=2\times3.14\times2m.[/tex]Simplifying the above result, we get:
[tex]C=12.56m.[/tex]Answer: [tex]\begin{equation*} 12.56m. \end{equation*}[/tex]I don’t understand the question its asking for the depth at 4 weeks and 9 weeks
Answer
Lake depth after 4 weeks: 343.6 ft
Lake depth after 9 weeks: 340.6 ft
Step-by-step explanation
The relation between time and lake depth is linear. Using the x-variable to represent time and the y-variable to represent the lake depth, we can use the next equation to relate these variables:
[tex]y=mx+b[/tex]where m is the slope and (0, b) is the y-intercept of the line.
The slope of the line that passes through the points (x₁, y₁) and (x₂, y₂) is calculated as follows:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]From the table, this line passes through (0, 346) and (2, 344.8), then its slope is:
[tex]m=\frac{344.8-346}{2-0}=\frac{-1.2}{2}=-0.6[/tex]From the table, this line passes through (0, 346), then parameter b is 346.
Substituting m = -0.6 and b = 346, the equation of the line is:
[tex]y=-0.6x+346[/tex]Evaluating this line at x = 4, that is, when time = 4 weeks, we get the next depth:
[tex]\begin{gathered} y=-0.6(4)+346 \\ y=-2.4+346 \\ y=343.6\text{ ft} \end{gathered}[/tex]Evaluating the equation of the line at x = 9, that is, when time = 9 weeks, we get the next depth:
[tex]\begin{gathered} y=-0.6(9)+346 \\ y=-5.4+346 \\ y=340.6\text{ ft} \end{gathered}[/tex]A 33-ft ladder leans against a building so that the angle between the ground and the ladder is 85°.how high does the ladder reach on the building ?
We have the next situation:
Now, we need to label the sides:
- The largest side is always the hypotenuse
- The adjacent side is between the right angle and the given angle.
- The opposite side is opposite to the given angle.
Hence,
Hypotenuse = 33 ftt
Opposite side = h
Then, we need to find h:
We need to use a trigonometric function that involves the side that we know and the missing side:
So,
sinθ = opposite side / hypotenuse
Replacing:
Sin85 = 33ft / h
Solve for h:
h= 33ft¨*sin 85
h= 32.87
The answer is 32.87
Instructions: Write the function in slope-intercept form that represents the given. The roasting guide for a turkey suggests cooking for 100 minutes plus an additional 8 minutes per pound (x). Write the equation for total cooking time in terms of pounds of turkey.
Answer:
y = 8x + 100
Explanation:
Let us call the total cooking time y and the x the number of pounds of turkey, then we know that the roasing guid
Help !!!! Please asap
Please only solve for angle 1 and ignore the question above.
Answer:
[tex]m\angle1\text{ = 115}\degree[/tex]Explanation:
Here, we want to get the value of the angle marked 1
From what we have, the bigger arc measures 236°
Now, we need to get the value of the arc ML
We have that as:
[tex]236-70-60\text{ = 106}\degree[/tex]Finally, we use one of the angle theorems to get the value
In using it, we have to consider the value of the smaller arc JK which is 124°
Now, we have its value as:
[tex]\frac{106\text{ + 124}}{2}\text{ = 115}\degree[/tex]We add the value of the arc ML and the value of the smaller arc JK and divide by 2
S/14 = 14 a. -196 b. 196 C. 28 d. 0
In the given equation, the value of S is divided by 14, so to calculate the value of S you have to invert the operation, that is, multiply it by 14 so that both operations cancel each other.
And, for the equality to be valid, all operations made in one side of the = sign must be done on the other side as well. So, multiply both sides of the equation by 14:
[tex]\begin{gathered} \frac{14S}{14}=14\cdot14 \\ S=196 \end{gathered}[/tex]S=196 the correct choise is b.
question will be in picture
given:
[tex]-7\le x[/tex]so, the line that represents the given inequality will be: b
What is the relationship between the pair of angles ABC and LMN shownin the diagram below?
Solution:
From the given figure
Where
[tex][/tex]What is the equation of the line that passes through the point (4, 9) with a slope of - 5/8 Write the equation in point-slope form.
the slope of the line is -5/8 and it is passing through (4, 9)
the equation of a line is
[tex]y-9=m(x-4)[/tex]put m = -5/8
[tex]\begin{gathered} y-9=-\frac{5}{8}(x-4) \\ y-9=-\frac{5}{8}x+\frac{1}{2} \end{gathered}[/tex]so the equation of line is
y = -5/8 x + (1/2) + 9
y = -5/8 x + 19/2
The bakery you choose cost $1000 per month to rent. The bakery that you almost rented was one fourth for the cost but was too small how much was the other bakery per month PLEASE HELPthis would be for a fifth grader and they have to show how they come up with the answer he would have to use the same scenario on multiple questions like this
The bakery you choose cost $1000 per month.
The bakery that you almost rented was one fourth for the cost: 1/4 of $1000.
When you have a fraction of a quantity you have to multiply the fraction by the value. Doing so, we have:
[tex]\begin{gathered} \frac{1}{4}\cdot1000 \\ \frac{1}{4}\cdot\frac{1000}{1}\text{ (Converting 1000 to a fraction)} \\ \frac{1000}{4}\text{ (Multiplying the numerators and then the denominators)} \\ 250\text{ (Dividing)} \\ \text{The answer is \$250} \end{gathered}[/tex]In an octagon, five of the angles are equal and each of the other three angles is 24° greater than each of the five other ones. Determine the angles of the octagon anto
Given:
5 angles are equal: x
Each of the other angles is 24 greater than the other 5 angles: x+24
An octagon has 8 angles; the sum of the interior angles of an octaogn is 1080º
[tex]5x+3(x+24)=1080º[/tex]Use the equation above to solve x:
[tex]\begin{gathered} 5x+3x+72=1080 \\ 8x+72=1080 \\ 8x=1080-72 \\ 8x=1008 \\ x=\frac{1008}{8} \\ \\ x=126 \end{gathered}[/tex]The 5 angles that are equal measure 126º
The other 3 angles measure:
[tex]x+24=126+24=150º[/tex]Then, the angles of the octagon are: 126º,126º,126º,126º,126º,150º,150º,150º6. Write a regression equation for the data above. (MD1)Answer of 5. is C.
Looking at the graph of item C in question 5, we can see that it is a straight line, so it is represented by a linear equation of the form:
[tex]y=mx+b[/tex]We can also see that, when the value of x increases, the value of y also increases, which means the slope of the line is positive (m > 0).
With this information and looking at the options, we can conclude that the correct option is B.
Miranda has $100.00 in a saving account that earns 10 percent interest, compounded annually. what wull the balance be after 1 year round to the nearest cent
solve equation. -2(y-1)=9
y = -7/2
Explanation:-2(y-1)=9
expand the bracket:
-2 × y -2 × -1 = 9
-2y + 2 = 9
collect like terms:
-2y = 9 -2
-2y = 7
Divide both sides by -2:
-2y/-2 = 7/-2
y = -7/2
In circle C with m BCD= 48°, find the angle measure of minor arc BD.DB
Notice that angle BCD is a central angle, therefore, the measure of its arc will be the same as the measure of the angle, therefore, the measure of the minor arc BD is 48 degrees
Lucille wrote three numbers between 0.75 and 0.76 what numbers could she have written?
As an answer to this question, any decimal between 0.75 and 0.76 will do.
So let us choose the three numbers at random.
0.751 , 0.754, and 0.756 will do.
5 lb of apples cost $8.20. How much is it for 1 lb?
The side walls of a regular quadrilateral pyramid are equilateral triangles with sides equal to 8 cm. Calculate the pyramid:1) the sum of the lengths of all the sides;2) the area of the base;3) the length of the height of the side wall;4) the area of the side wall.
a) 64cm
b) 64 square cm
c) 4√3 cm
d) 16√3 square cm
Explanations:A regular quadrilateral pyramid with equilateral triangles is as shown below;
1) The pyramid has 8 side lengths, hence the sum of the length of all the sides is given as:
[tex]\begin{gathered} Sum\text{ of side lengths}=8\times8cm \\ Sum\text{ of side lengths}=64cm \end{gathered}[/tex]2) Since the triangular sides are equilateral, the base of the pyramid will be a square with side length of 8cm. The area of the base is expressed as:
[tex]\begin{gathered} A=length\times length \\ A=8cm\times8cm \\ A=64cm^2 \end{gathered}[/tex]3) Since one side wall is an equilateral triangle, the height will be perpendicular to the base as shown:
In order to determine the height, we will use the Pythagorean theorem as shown:
[tex]\begin{gathered} 8^2=h^2+4^2 \\ h^2=8^2-4^2 \\ h^2=64-16 \\ h^2=48 \\ h=\sqrt{48}=4\sqrt{3}cm \\ \end{gathered}[/tex]4) The area of the side wall is equivalent to the area of the triangle expressed as:
[tex]\begin{gathered} Area\text{ of side wall}=\frac{1}{2}\times base\times height \\ Area\text{ of side wall}=\frac{1}{2}\times8cm\times4\sqrt{3} \\ Area\text{ of side wall}=16\sqrt{3}cm^2 \end{gathered}[/tex]