The equation of the linear function is f(x) = (31/5)x - 660.
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
We have,
Let the equation be:
f(x) y = ax + m
Now,
The linear function:
f(300) = 1200
f(800) = 4300
This can be written as:
1200 = 300a + m ____(1)
4300 = 800a + m ______(2)
From (1) we get,
m = 1200 - 300a _____(3)
Putting (3) in (2) we get,
4300 = 800a + 1200 - 300x
4300 = 500a + 1200
4300 - 1200 = 500a
3100 = 500a
a = 31/5
Now,
m = 1200 - 300a
m = 1200 - 300 x 31/5
m = 1200 - 60 x 31
m = 1200 - 1860
m = - 660
The equation can be written as:
f(x) = (31/5)x - 660
We can cross-check:
f(300):
= (31/5) x 300 - 660
= 31 x 60 - 660
= 1860 - 660
= 1200
Thus,
The equation of the linear function is f(x) = (31/5)x - 660.
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The radius of a sphere is 4 inches. If the radius is doubled, how does that change the surface area of the sphere?aThe surface area is multiplied by fourbThe surface area is squaredcThe surface area is doubleddThe surface area is multiplied by eight
Solution:
Given the radius of the sphere is 4inches.
The surface area, A, of the sphere is;
[tex]\begin{gathered} A=4\pi r^2 \\ \\ A=4\pi(4^2) \\ \\ A=201.06in^2 \end{gathered}[/tex]But when the radius is doubled;
[tex]\begin{gathered} r=8in \\ \\ A=4\pi(8^2) \\ \\ A=804.25in^2 \end{gathered}[/tex]Hence, when the radius is doubled, the surface area is multiplied by four.
y= 2000 cos π/14 (8-4)
Solve the equation
First step is to find cos (pi/14), then solve the product)
[tex]\begin{gathered} y=2000\cdot\cos (\frac{\pi}{14})\cdot(8-4) \\ y=2000\cdot0.9749\cdot(4) \\ y=7799.42 \end{gathered}[/tex]I need help figuring out what angle these degrees are
1) Looking at the picture we can state that
m∠1 = 57º and m∠2 = 180-57
m∠2 = 123º
We can state that according to the Same side interior angles that states that those angles ∠1 , and ∠2 are supplementary since those angles belong to lines that have been crossed by a transversal line t.
Given vector u equals open angled bracket 8 comma negative 6 close angled bracket and vector v equals open angled bracket negative 5 comma 2 close angled bracket comma what is v − u?
Answer:
<-13, 8>
Explanation:
Given vectors u and v below:
[tex]\begin{gathered} u=\langle8,-6\rangle \\ v=\langle-5,2\rangle \end{gathered}[/tex]In order to evaluate v-u, subtract the corresponding elements as follows:
[tex]\begin{gathered} v-u=\langle-5,2\rangle-\langle8,-6\rangle \\ =\langle-5-8,2-(-6)\rangle \\ =\langle-13,2+6\rangle \\ v-u=\langle-13,8\rangle \end{gathered}[/tex]The third option is correct.
Solve the following system hood equations by the substitution method
Question:
Solution:
Consider the following system of linear equations:
Equation 1:
[tex]6x+7y=17[/tex]Equation 2:
[tex]x=22-5y[/tex]Replacing the above equation into equation 1, we get:
[tex]6(22-5y)+7y=17[/tex]Applying the distributive property, we get:
[tex]132-30y+7y=17[/tex]this is equivalent to:
[tex]-30y+7y=17-132[/tex]this is equivalent to:
[tex]-23y=\text{ -115}[/tex]or
[tex]23y=\text{ 115}[/tex]solving for y, we obtain:
[tex]y=\frac{115}{23}=5[/tex]Now, replacing this into Equation 2, we obtain:
[tex]x=22-5(5)=22-25=-3[/tex]So that, we can conclude that the correct answer is:
The solution is (-3, 5)
A number c is no less than -1.5 and less than 5.3
Step-by-step explanation/answer:
A number c is no less than -1.5 and less than 5.3.
So -1.5<= c < 5.3
You would label your number line and have a filled in closed circle at -1.5 and an open circle at 5.3 to signify that 5.3 is not a possible value of c.
Perform the indicated operation. 22 6/11 x 1 1/2
Answer:
[tex]1\frac{1}{2}[/tex] <2<2 [tex]\frac{6}{11}[/tex]
Step-by-step explanation:
[tex]1\frac{1}{2}[/tex] is less than 2 is less than 2 [tex]\frac{6}{11}[/tex]
[tex]\frac{33}{22} < \frac{44}{22} < \frac{56}{22}[/tex]
Peaches cost $4 for a 7-pound bag. If grapes cost 15% less per pound and oranges cost 35% more per pound than peaches, which of the following could be the price per pound of grapes and oranges?
A. Grapes are $0.43 per pound and oranges are $0.82 per pound
B. Grapes are $0.48 per pound and oranges are $0.77 per pound
C. Grapes are $0.57 per pound and oranges are $0.77 per pound
D. Grapes are $0.38 per pound and oranges are $0.87 per pound
C. Grapes are $0.48 per pound and oranges are $0.77 per pound.
The cost of grapes and oranges are 0.48 and 0.77 respectively.
Cost word problem
Evaluating cost of solution is simple: You determine the time and money you need to develop and implement it. You're looking at the resources needed. Cost of problem, however, equals the price of doing nothing. That is, for what I know, an important economic principle known from cost-benefit analyses.
Given that Peaches cost $4 for a 7-pound bag, grapes cost 15% less per pound than peaches, oranges cost 35% more per pound than peaches.
Cost of 7 pounds of peaches = 4
Therefore cost of 1 pound of peaches = 4/7 = 0.57
Cost of one pound of grapes = 0.57 - 15% of 0.57
= 0.57 - 0.0855
= 0.4845
= 0.48
Cost of one pound of oranges = 0.57 + 35% of 0.57
= 0.57 + 0.1995
= 0.7695
= 0.77
Therefore Grapes are $0.48 per pound and oranges are $0.77 per pound.
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solve for the unknown angle measure given that f || g
The measure of the unknown angle is 75°
What is an angle?
An angle is a shape in Euclidean space created by two rays, termed the ends of the angle, that share a common termination, called the vertex of the angle. Angles produced by two rays are located in the longitudinal plane the rays. Angles are also generated when two planes overlap. These are known as dihedral angles. An angle defined by two intersecting curves is the angle of the rays lying tangent to the respective curves at their point of junction. Angle can also refer to the measurement of an angle or of a rotation. In the case of a geometric angle, the arc is defined by the sides and is centered at the vertex.
From figure,
x+70+25 = 180 (angle sum property of a triangle)
x = 180 - 95 = 75°
Hence, the measure of the unknown angle is 75°
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what else would need to be congruent to show that triangle ABC=DEF
(AAS): If two angles and the non-included side of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent
Identify two similar triangles in the figure below, and complete the explanation of why they are similar. Then find AB. B А C 21 D ZA = (select) and ZABD = (select), so ABD - ACB by the (select)y Triangle Similarity Theorem. AB =
Answer:
∠A ≅ ∠A and ∠ABD ≅ ∠ACB, so ΔABD ≅ ΔACB by the AA (Angle - Angle) Triangle Similarity Theorem.
AB = 10
Explanation:
An angle is congruent to itself, so ∠A ≅ ∠A
On the other hand, taking into account the representation of the angles, we can say that: ∠ABD ≅ ∠ACB
Then, the triangles ABD and ACB are congruent by the AA (Angle-Angle) triangle similarity theorem because we have two congruent angles:
∠A ≅ ∠A
∠ABD ≅ ∠ACB
Now, if two triangles are similar their corresponding sides are proportional.
So, we can formulate the following equation:
[tex]\frac{AB}{AC}=\frac{AD}{AB}[/tex]Then, replacing AC by (21 + 4), AD by 4, and solving for AB, we get:
[tex]\begin{gathered} \frac{AB}{21+4}=\frac{4}{AB} \\ AB\times AB=4(21+4) \\ AB^2=4(25) \\ AB^2=100 \\ AB=\sqrt[]{100} \\ AB=10 \end{gathered}[/tex]Therefore, the answers are:
∠A ≅ ∠A and ∠ABD ≅ ∠ACB, so ΔABD ≅ ΔACB by the AA (Angle - Angle) Triangle Similarity Theorem.
AB = 10
Solve this equation: 80 = 3y + 2y + 4 + 1. O A. y = ¹1/5 O B. y = 75 O C. y = 15 O D.y = -15
Answer:
C. y= 15
Step-by-step explanation:
Add 3y +2y = 5y
Add 4+1=5
Subtract 80 -5 =75
Then divide by 5y on both sides to get
y=15
What is the value of 24 - 5²?Record your answer and fill in thebubbles on your answer document.Be sure to use the correct placevalue.
24 - 5²
24 - 25 (Raising 5 to the power of 2)
-1 (Subtracting)
The answer is -1.
-12- (-35)
Enter the correct answer in the box.What are the solutions of this quadratic equation?1 2 = 161 – 65Substitute the values of a and b to complete the solutions.TIsin cos tan sin-costan-1α βhaE908 001vo yoΖΔfo?X• Dlot<λμ ρ>CSC seccot log logIn=x= a + bix=a-biResetNext
Given the equation
[tex]x^2=16x-65[/tex]To find a and b, you have to find the roots, following the steps below.
Step 01: Write the equation in the general quadratic form.
The general quadratic form is ax²+bx+c=0.
Then, add -16x + 65 to both sides of the equation.
[tex]\begin{gathered} x^2-16+65=16x-65-16x+65 \\ x^2-16+65=0 \end{gathered}[/tex]Step 2: Use the Bhaskara formula to find the roots.
The Bhaskara formula for a general equation is:
[tex]x=\frac{-b\pm\sqrt[]{b^2-4\cdot a\cdot c}}{2\cdot a}[/tex]In this exercise,
a = 1
b = -16
c = 65
Then,
[tex]\begin{gathered} x=\frac{-(-16)\pm\sqrt[]{(-16)^2-4\cdot1\cdot65}}{2\cdot1} \\ x=\frac{+16\pm\sqrt[]{256-260}}{2} \\ x=\frac{+16\pm\sqrt[]{-4}}{2} \end{gathered}[/tex]√-4 can also be written as:
[tex]\sqrt[]{-4}=\sqrt[]{(4)\cdot(-1)}=\sqrt[]{4}\cdot\sqrt[]{-1}[/tex]Knowing that i = √-1:
[tex]\sqrt[]{-4}=\sqrt[]{4}\cdot i[/tex]Then:
[tex]\begin{gathered} x=\frac{+16\pm\sqrt[]{-4}}{2}=\frac{+16\pm\sqrt[]{4}\cdot i}{2} \\ x=\frac{16\pm2\cdot i}{2} \\ x=\frac{16}{2}\pm\frac{2}{2}\cdot i \\ x=8\pm i \end{gathered}[/tex]The roots are:
8 + 1i
8 - 1i
So, the Answer is:
a = 8
b = 1
Limit as x approaches infinity of 4^x
The limit as x approaches infinity of 4^x is of infinity, that is:
[tex]\lim_{x \rightarrow \infty} 4^x = \infty[/tex]
How to calculate the limit of a function?The first step in calculating the limit of a function is calculating the numeric value of the function at the value of x which the function approaches.
In this problem, the limit is given as follows:
[tex]\lim_{x \rightarrow \infty} 4^x = 4^{\infty} = \infty[/tex]
There is nothing undetermined, hence the value of limit is of infinity, as we calculated.
If an undetermined value such as 0/0 or infinity/infinity had been reached, then alternatives such as factorization or L'Hospital rule would be searched, but is not necessary in the context of this problem.
Hence, the limit is of infinity.
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Alana has 12.5 cups of flour with which she is baking four loaves of raisin bread and one large pretzel. The pretzel requires 2.5 cups of flour to make. How much flour is in each loaf of raisin bread? Explain the steps to follow to get the answer.
what does it mean to subtract 4 on both sides of 76 equals 7 and 2x
Question 20 of 25If AABC is similar to ADEF, the sides of AABC must be congruent to thecorresponding sides of ADEF.OA. TrueOB. False
Given: If triangle ABC is similar to triangle DEF, the sides of triangle ABC must be congruent to the corresponding sides of triangle DEF.
Required: To determine if the given statement is true or false.
Explanation: If two triangles are similar, then their corresponding sides are in equal proportion. So, if triangle ABC is similar to triangle DEF then
[tex]\frac{AB}{DE}=\frac{BC}{EF}=\frac{AC}{DF}[/tex]Final Answer: Option B, False is correct.
#3 list the angles of each triangle in order from smallest to biggest
Statement Problem: (3)
List the angles of the triangle in order from smallest to largest.
Solution:
First, let's use the Cosine Rule to find the angle B;
[tex]\begin{gathered} b^2=a^2+c^2-2ac\cos B \\ 2ac\cos B=a^2+c^2-b^2 \\ \cos B=\frac{a^2+c^2-b^2}{2ac} \end{gathered}[/tex]Where;
[tex]\begin{gathered} a=3,b=2.9,c=3.1 \\ \cos B=\frac{3^2+3.1^2-2.9^2}{2(3)(3.1)} \\ \cos B=\frac{9+9.61-8.41}{18.6} \\ \cos B=\frac{10.2}{18.6} \\ \cos B=0.5484 \\ B=\cos ^{-1}(0.5484) \\ B=56.74 \\ B=57^o \end{gathered}[/tex]Also, let's use the Cosine Rule to find the angle A;
[tex]\begin{gathered} a^2=b^2+c^2-2bc\cos A \\ \cos A=\frac{b^2+c^2-a^2}{2bc} \end{gathered}[/tex][tex]\begin{gathered} \cos A=\frac{2.9^2+3.1^2-3^2}{2(2.9)(3.1)} \\ \cos A=\frac{8.41+9.61-9}{17.98} \\ \cos A=\frac{9.02}{17.68} \\ A=\cos ^{-1}(0.5102) \\ A=59.32 \\ A=59^o \end{gathered}[/tex]Lastly, let's use the sum of angles in a triangle theorem to get the third angle, Angle C;
[tex]\begin{gathered} \angle A+\angle B+\angle C=180^o \\ \angle C=180^o-59^o-57^o \\ \angle C=64^o \end{gathered}[/tex]Hence, the angles of the triangle from the smallest to the largest are;
[tex]\angle B,\angle A,\angle C[/tex]Angle B,
Angle A,
Angle C
need to know the steps and how to work it out to get the correct anwser
Given equation:
[tex]\text{y = -x + 1}[/tex]For two lines to be parallel, the slope of one will be the same as the slope of the second line
[tex]\begin{gathered} u\sin g\text{ equation of line:} \\ y\text{ = mx + b} \\ m\text{ = slope, b = y-intercept} \end{gathered}[/tex]comparing the given equation with the equation of line:
[tex]\begin{gathered} y\text{ = y} \\ mx\text{ = -x = -1(x)} \\ m\text{ = -1} \\ b\text{ = 1} \end{gathered}[/tex]This means the slope of the 1st line is -1. The slope of the second line will also be -1 since they are parallel
To get the y-intercept of the second line, we would insert the slope and the point given:
point given: (-7, 3) = (x, y)
[tex]\begin{gathered} y\text{ = mx + b} \\ 3\text{ = -1(-7) + b} \\ 3\text{ = 7 + b} \\ 3\text{ - 7 = b} \\ b\text{ = -4} \\ y-\text{intercept of 2nd line = -4} \end{gathered}[/tex]The second equation is the equation of line that is parallel to the line y = -x + 1 and passes through (-7, 3)
Second equation:
[tex]\begin{gathered} y\text{ = mx + b} \\ y\text{ = -1(x) + (-4)} \\ y\text{ = -x - 4} \end{gathered}[/tex][tex]\begin{gathered} In\text{ slope intercept form:} \\ y\text{ = -x - 4} \end{gathered}[/tex]If 6 times a number is decreased by 2, the principal square root of this difference is 3 less than the number. Find the number(s).
So first we have the expression "six times a number". Let's use x to designate the number, then this expression can be written as 6x. We are being told that this term is decresed by 2 which means that now we have 6x-2. Then we have a certain condition on the principal square root, this would be:
[tex]\sqrt[]{6x-2}[/tex]We are being told that this square root is equal to "3 less than the number". This last term can be written as x-3. Knowing that x-3 has to be equal to the square root I mentioned before we can build an equation for x:
[tex]\sqrt[]{6x-2}=x-3[/tex]Know let's find x. First I'm going to get rid of the square root by squaring both sides of the equation:
[tex]\begin{gathered} (\sqrt[]{6x-2})^2=6x-2=(x-3)^2 \\ 6x-2=(x-3)^2=x^2-6x+9 \\ 6x-2=x^2-6x+9 \end{gathered}[/tex]Know let's move all terms to the right side:
[tex]\begin{gathered} 6x-2=x^2-6x+9 \\ 0=x^2-6x+9-6x+2 \\ 0=x^2-12x+11 \end{gathered}[/tex]So we have a cuadratic function equalizing 0. This means that we can use the cuadratic formula:
Where a, b and c are the coefficients of the cuadratic equation.In this case a=1, b=-12 and c=11 so we have:
[tex]\begin{gathered} x=\frac{-(-12)\pm\sqrt[]{(-12)^2-4\cdot1\cdot11}}{2\cdot1}=\frac{12\pm\sqrt[]{144-44}}{2}=\frac{12\pm\sqrt[]{100}}{2} \\ x=\frac{12\pm10}{2}=6\pm5 \end{gathered}[/tex]So we have two possible values for x, 1 and 11. Then the solution set is {1,11}
8. 500 Vanessa is in charge of organizing volunteers to make sandwiches to feed the homeless during the Memorial Day weekend. She needs to have 500 sandwiches made so she will want to get the help of as many volunteers as possible to assist her and the 3 other paid staff who will also be making the sandwiches. Use the function s(v) = to determine s(v), the number of sandwiches each person will have to make based on v, the number of volunteers working.
ANSWER
EXPLANATION
In this problem, we have to complete the table by replacing v with each value from 0 to 6 in the table, and compute the corresponding value of s(v) based on the equation,
[tex]s(v)=\frac{500}{v+4}[/tex]Find the values for the table,
[tex]v=0;s(0)=\frac{500}{0+4}=\frac{500}{4}=125[/tex][tex]v=1;s(1)=\frac{500}{1+4}=\frac{500}{5}=100[/tex][tex]v=2;s(2)=\frac{500}{2+4}=\frac{500}{6}\approx83.3[/tex][tex]v=3;s(3)=\frac{500}{3+4}=\frac{500}{7}\approx71.4[/tex][tex]v=4;s(4)=\frac{500}{4+4}=\frac{500}{8}=62.5[/tex][tex]v=5;s(5)=\frac{500}{5+4}=\frac{500}{9}\approx55.6[/tex][tex]v=6;s(6)=\frac{500}{6+4}=\frac{500}{10}=50[/tex]Need helpQuick answer is okay. I will attach the other photos.
SOLUTION
The graph of
[tex]f(x)=\frac{1}{4}(3)^x[/tex]is shown below
Comparing to the options, the answer is option D
Use the transformations of the graph of f(x) = x^2 to determine the graph of the function. h(x) = -(x+2)^2
Answer:
Step-by-step explanation:
The graph f(x) = x^2 is shifted along the OX axis to the left by 2 and reflected relative to this axis:
Giselle works as a carpenter and as
a
blacksmith.
She earns $20 per hour as a carpenter and $25
per hour as a blacksmith. Last week, Giselle
worked both jobs for a total of 30 hours, and
earned a total of $690.
How long did Giselle work as a carpenter
last week, and how long did she work as a
blacksmith?
Answer:
Step-by-step explanation:
$20/hr carpenter pay
$25/hr blacksmith pay
Let c = hours working carpentry
Let b = hours working as blacksmith
c + b = 30 {equation 1}
20c + 25b = 690 {equation 2}
In equation 1 solve for one variable in terms of the other.
c = 30-b
Substitute that into equation 2:
20(30-b) + 25b = 690
600 - 20b + 25b = 690
5b = 90
b = 90/5
b = 18 hours working as a blacksmith
c = 30-b = 30-18 = 12 hours as a carpenter
Answer:
she worked as a carpenter for 12 hours
And a blacksmith for 18 hours
Step-by-step explanation:
B=hours as blacksmith
C=hours as carpenter
20c+25b=690
b+c=30
c=30-b
So we substitute this into the first equation
20(30-b)+25b=690
600-20b+25b=690
5b=90
B= 18
18+c=30
C=12
Use synthetic division to divide.
(-4x3 - 22x2 - 12x - 10) ÷ (x + 5)
Answer:
-4x² - 2x - 2
Step-by-step explanation:
(-4x3 - 22x2 - 12x - 10) ÷ (x + 5)
-5 | -4 -22 -12 -10
↓ 20 10 10
-----------------------------------
-4 -2 -2 0
-4x² - 2x - 2
I hope this helps!
Use the connect line tool to draw your path so that it meets the requirements. Then drag water fountains to the map and place them along the path based on the requirements. Diagonal lines may not be used.
1 mile is equivalent to 5280 feet which is equivalent to 5280/440 in = 12 in
Hence, a path of 2miles is equivalent to 24 in on the graph
The connect line is as shown in the image from the School to the Park and it is colored red and 24 in long.
The position of the water fountains are marked in pink on the graph,
The first is 1/3 of the way from the School which is 8 in from the school.
The second is 2/3 of the way from the School which is 16 in from the school.
A cylindrical vase has a circumference of about 62.8 centimeters and a height of 33 centimeters. To the nearest cubic centimeter, how much water will the vase hold?
The volume of water that the cylindrical vase can hold is 10362 cm³.
Volume is a measurement of three-dimensional space that is occupied. It is frequently expressed mathematically using imperial or SI-derived units. Volume and the notion of length are connected.
The circumference of a cylindrical vase is 62.8 centimeters.
The height of the cylindrical vase is 33 centimeters.
Let r be the radius of the cylinder.
The circumference of the cylinder is given as:
C = 2πr
62.8 cm = 2 × 3.14 × r
r = 10 cm
The volume of a cylinder is given as:
V = πr²h where r is the radius and h is the height of the cylinder
Then,
V = 3.14 × ( 10 )² × 33
V = 10362 cm³
Hence, the cylindrical vase can hold 10362 cm³ of water.
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Answer: Bro above is wrong it's 10,367 cm3 PLATO
Step-by-step explanation: mad maths skills
Ed has a total of 92 coins in his collection.This is 8 more than three times the number of dimes in his collection. How many dimes does Ed have in his collection ? write and solve and equation
Let x represent the number of dimes Ed has in its collection.
The total of coins in the collection is 8 more than three times the number of dimes.
The number of coins is 92.
3 times the number of dimes can be symbolized as: 3x
"8 more" is symbolized as +8
So the total number of coins equals:
92=3x+8
From this expression you can determine the number of dimes by solving the equation for x:
[tex]\begin{gathered} 92=3x+8 \\ 92-8=3x \\ 84=3x \\ \frac{84}{3}=\frac{3x}{3} \\ 28=x \end{gathered}[/tex]x=28 → Ed has 28 dimes in his collection.
Andre and Elena are reading the same book over the 1 summer. Andre says he has read 1/5 of the book. Elena ! says she has read 20 more pages than Andre. If Elena is on page 55, how many pages are in the book? Lin has drawn a diagram to solve this question. Find her error..
Answer:
The book has 175 pages
Explanation:
Andre says that he has read 1/5 of the book, so the correct diagram should have each rectangle label as a (the number of pages that Andre has read)
because 5 times 1/5 of the book makes the complete book.
On the other side, Elena has read 20 more pages than Andre, so we should have the second rectangle divided and one part should be label as 20 and the sum of a and 20 is equal to 55.
So, the correct diagram is:
Therefore, we can calculate the number of pages that Andre has read as:
a = 55 - 20 = 35
Then, the number of pages of the book is 5 times a, so:
5 x a = 5 x 35 = 175
Therefore, the answer is the book has 175 pages
