The vertex of the parabola y = (x – 5)² + 8 with a vertical axis of symmetry is the point (5, 8).
Explanation:The question is asking for the vertex of the parabola y = (x − 5)² + 8 which has a vertical axis of symmetry. In the general equation for a parabola, y - k = a(x - h)², the vertex is denoted by the (h, k). So, comparing this with the given parabola equation, we can determine that the h value corresponds to the value inside the brackets in the (x – h)² part of the equation, and the k value corresponds to the term added or subtracted outside the squared term.
For the given equation, y = (x – 5)² + 8, we can see that h = 5 and k = 8. Therefore, the vertex of the parabola is at the point (5, 8).
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Can someone please help
Suppose 6 quarts of milk cost $5.10. Use the unit price (price per quart) to determine how much 5 gallons of milk cost?
A $17.00
B $34.00
C $8.50
D $0.85
E $4.25
Answer:
Answer is: A
Step-by-step explanation:
Because it is.
Answer:
A. $17.00
Step-by-step explanation:
$5.10 for 6 quarts.
Unit cost: ($5.10)/(6 qt) = $0.85/qt
Price for 5 gallons:
1 gallon = 4 quarts
5 gallons = 5 * 4 quarts = 20 quarts
Price for 5 gallons = unit price * number of quarts
Price for 5 gallons = $0.85/qt * 20 qt = $17.00
Answer: A. $17.00
On the model scale drawing, approximately how far should each edge of the bed be from its own corner of the wall? Use complete sentences to explain your reasoning.
Solution:
Considering room to be in the shape of Cuboid as well as the Bed to be in the shape of Cuboid.
Dimensions of Room
Let Length of cuboid which is in the shape of room = L
Breadth of cuboid which is in the shape of room = B
Height of cuboid which is in the shape of room = H
Considering, L>B>H
Dimension of Bed
Length=[tex]\frac{L}{6}[/tex] units
Breadth=[tex]\frac{B}{4}[/tex] units
Height=[tex]\frac{H}{6}[/tex] units
Taking one corner at origin i.e (0,0,0)
You can keep your bed at any place inside the room, but you want your bed to be at that place inside the room where the window is located so that proper ventilation and sunlight can enter your room.
Taking bed to be in the middle of room near the window and considering it's upper face
Distance from one corner i.e from length= B- [tex]\frac{B}{4}[/tex]=[tex]\frac{3B}{4}[/tex] Units
Distance from other corner= 0 Units
Distance from Breadth of one side of wall= [tex]\frac{L}{3}[/tex] units
Distance from one corner i.e from Breadth =L - [tex]\frac{L}{3}[/tex]-[tex]\frac{L}{6}[/tex]= [tex]\frac{L}{2}[/tex]
Distance from floor i.e surface=[tex]\frac{H}{6}[/tex] units
Distance from Ceiling= H -[tex]\frac{H}{6}[/tex] = [tex]\frac{5 H}{6}[/tex] units
To find the distance each bed edge should be from the corner in a scale drawing, determine the scale used (such as 1 inch = 6 feet), convert actual bed dimensions using the scale, and ensure measurements on the drawing are precise and noted with the correct line types.
To determine how far each edge of the bed should be from its own corner of the wall in a scale drawing, first establish the scale being used for the model. For example, if the scale is 1 inch = 6 feet, convert the actual dimensions of the bed into the scale size by using ratios that compare the scale distance to the actual distance. If the actual bed is 6 feet long, then the length on the scale model would be 1 inch. When recording measurements, both the actual size and the scale size should be clearly marked to prevent confusion. It is important to use correct line types and to make all the drawings to exact measurements within the constraints of the paper size.
For consistent and accurate representation, the edges of the bed should be measured from the corner of the walls based on the determined scale. This involves calculating the distance of the bed from the wall in actual size, then converting that distance to the scale model size. Pay attention to significant figures and the choice of units (inches, feet, centimeters, meters) to maintain precision in your scale drawing.
Jay is 4 years younger than three times Tamia's age. Jay is 20 years old. How old is Tamia?
Final answer:
To find Tamia's age, an equation was set up based on the relationship between Jay and Tamia's ages. Jay is 20 years old and 4 years younger than three times Tamia's age. Solving the equation shows that Tamia is 8 years old.
Explanation:
Jay is 4 years younger than three times Tamia's age. Given that Jay is 20 years old, we can use this information to find out how old Tamia is. Let's denote Tamia's age as T. The relationship between their ages can be represented by the equation: Jay's age = 3 × Tamia's age - 4. Since Jay's age is 20, we can substitute this into the equation, giving us 20 = 3T - 4.
To solve for T, we first add 4 to both sides of the equation, which gives us 24 = 3T. Next, we divide both sides by 3 to find Tamia's age, resulting in T = 8. Therefore, Tamia is 8 years old.
This problem was solved by setting up an equation based on the relationship described between Jay and Tamia's ages, then using basic algebraic steps to solve for Tamia's age.
Find the value of x in this figure.
A) 43
B) 47
C) 53
D) 57
Answer: 47 (choice B)
x+43 = 90
x = 90 - 43
x = 47
This works because triangle PQR is a right triangle (with angle Q as the 90 degree angle). We say that that P and R are complementary angles. I added point R to be located where the angle x is written.
Answer:
47
Step-by-step explanation:
Lalo has 1,500 minutes per month on his cell phone plan. How many more minutes can he use if he has already talked for 785 minutes in an inequality? Explain.
Answer:
All you have to do is subtract 1500-785 in order to find the number of minutes left for him.
1500-785=715 more minutes left
suppose that there are two types of tickets to a show: advance and same day. Advance tickets cost $20 and same-day tickets cost $25. For one performance, there were 75 tickets sold in all, and the total amount paid for them was $1700. how many of each type were sold?
How do I multiply (4-√2)(5+√3)
Answer:
17.4076456756
Step-by-step explanation:
SOS HURRY
The vertices of a square are (-5,-4) (-2,-8) (1,-4) (-2,0) What is the area of the square?
First, by using the distance formula for just one side, we can find the length of all sides (a square has 4 equal sides.) Then, we can apply the area of a square formula, which is a^2.
Distance formula:
[tex]\sqrt{(x.2 - x.1)^{2} + (y.2 - y.1)^{2}}[/tex]
√((-2 + 5)^2 + (-8 + 4)^2)
√((3)^2 + (4)^2)
√9 + 16
√25
5
The side lengths of the square are each equal to 5, and by applying the formula for area, we can find the area of the square.
5^2 = 25
The area is 25.Which value is equivalent to 48 ÷ ((2 + 6) × 2) − 1? A) -12 B) 2 C) 3 1 5 D) 3
Answer:
B) 2
Step-by-step explanation:
Given expression,
48 ÷ ((2 + 6) × 2) − 1
In simplification we follows the following order,
B = Bracket
O = Of
D = Division
M = Multiplication
A = Addition,
S = Subtraction,
Thus, steps of solving the given expression by following BODMAS are as follow,
[tex]\frac{48}{(2 + 6) \times 2}-1[/tex]
[tex]=\frac{48}{8\times 2}-1[/tex]
[tex]=\frac{48}{16}-1[/tex]
[tex]=3-1[/tex]
[tex]=2[/tex]
Hence, OPTION B is correct.
The value equivalent to 48 ÷ ((2 + 6) × 2) - 1 is B) 2.
Explanation:To solve this problem, we need to follow the order of operations (also known as PEMDAS or BODMAS).
First, we calculate the expression inside the parentheses: 2 + 6 = 8.
Next, we multiply the result by 2: 8 × 2 = 16.
Finally, we divide 48 by the result: 48 ÷ 16 = 3.
After that, we subtract 1: 3 - 1 = 2.
Therefore, the value equivalent to 48 ÷ ((2 + 6) × 2) - 1 is 2.
Which points are on the graph of g(x)=(1/5)x
Select EACH CORRECT ANSWER
If a point is on the graph of the exponential equation then it should be true when you solve.
g(x) = (1/5)^x
y = (1/5)^x
1/125 = (1/5)^3
cbrt(1/125) = 1/5
.2 = 1/5
.2 = .2 YES
5 = (1/5)^-1
5 = 5 YES
1/25 = (1/5)^-2
-2root(1/25) = 1/5
5 = 1/5 NO
0 = (1/5)^1
0 = .2 NO
The correct answers are A and B.
This is about understanding input and output of a graph.
Correct Points are;
Option B; (-1, 5) and Option A; (3, 1/125)
The graph function is given as; g(x) = (1/5)ˣ
x is the input value which is on the x-axis
g(x) is the output value which is on the y-axis
This will follow a coordinate writing system of (x, y)
Option A; (3, 1/125) means that when x = 3, y = 1/125Let us put 3 for x in the function;
y = (1/5)³
y = 1/125
y = 1/125 corresponds to y = 1/125 and so it is correct.
Option B; (-1, 5) means that when x = -1, y = 5
Let us put -1 for x in the function;
y = (1/5)⁻¹
y = 5
y = 5 corresponds to y = 5 and so it is correct.
Option C; (-2, 1/25) means that when x = -2, y = 1/25Let us put 3 for x in the function;
y = (1/5)⁻²
y = 25
y = 1/25 doesn't correspond to y = 25 and so it is not correct.
Option D; (1, 0) means that when x = 1, y = 0Let us put 1 for x in the function;
y = (1/5)¹
y = 1/5
y = 0 doesn't correspond to y = 1/5 and so it is not correct.
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can some one help me. Solve this equation.
[tex]\bold{Given : 2^2^x^-^2 - 2^x^-^1 = 2^x - 2}[/tex]
[tex]\bold{\implies (2^2^x) (2^-^2) - (2^x)(2^-^1) = 2^x - 2}[/tex]
[tex]\bold{\implies \frac{(2^2^x)}{(2^2)} - \frac{(2^x)}{(2^1)} = 2^x - 2}[/tex]
[tex]\bold{\implies \frac{(2^2^x)}{4} - \frac{(2^x)}{2} = 2^x - 2}[/tex]
[tex]\bold{\implies \frac{[2^2^x - (2^x)(2)]}{4} = 2^x - 2}[/tex]
[tex]\bold{\implies [2^2^x - (2^x)(2)] = (4)(2^x) - 8}[/tex]
[tex]\bold{\implies 2^2^x - (2^x)(2) - (4)(2^x) + 8 = 0}[/tex]
[tex]\bold{\implies (2^x)^2 - (2^x)(6) + 8 = 0}[/tex]
[tex]\bold{Let\;us\;take : (2^x) = Z}[/tex]
[tex]\bold{\implies Z^2 - 6Z + 8 = 0}[/tex]
[tex]\bold{\implies Z^2 - 4Z - 2Z + 8 = 0}[/tex]
[tex]\bold{\implies Z(Z - 4) - 2(Z - 4) = 0}[/tex]
[tex]\bold{\implies Z = 4\;\;(or)\;\;Z = 2}[/tex]
[tex]\bold{But : Z = 2^x}[/tex]
[tex]\bold{\implies 2^x = 4\;\; (or) \;\; 2^x = 2}[/tex]
[tex]\bold{\implies 2^x = 2^2\;\; (or) \;\; 2^x = 2^1}[/tex]
[tex]\bold{\implies x = 2\;\;(or)\;\; x = 1}[/tex]
A graduated cylinder is filled with 36pi cm^3 of liquid. The liquid is poured into a different cylinder that has a radius of 3 cm.
What will the height of the liquid be in the new cylinder?
___cm
PLZ HELP ME I WILL MARK U as the brainliest answerrrrr I cannot get this wrong PLZZ
The liquid height in the new cylinder will be 4 cm after the volume of liquid from the original cylinder is transferred.
Explanation:In the context of this problem, we are dealing with the concept of the volume of a cylinder. The volume of a cylinder is given by the formula V=πr²h, where r is the radius of the base and h is the height of the cylinder. The given volume in the problem is 36π cm³ and the radius of the second cylinder is 3 cm. We will use the volume formula to find the height.
We know that V=36π cm³ and r=3 cm. Substituting these values into the volume formula, we get 36π=π(3)²h. Simplifying the equation gives us 36π=9πh. Dividing both sides by 9π, we arrive at the solution, h=4 cm. Therefore, the height of the liquid in the new cylinder will be 4 cm.
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Three geometric sequences are given below.
Sequence A: 160,40,10,2.5,...
Sequence B: -21,63,-189,567,...
Sequence C: 8,12,18,27,....
Order the sequences from least common ratio to the greatest common ratio.
Answer:
A C B
Step-by-step explanation:
In sequence A. the numbers are being divided by 4.
In sequence B. the numbers are being multiplied by -3
In sequence C. the numbers are being add by 4
So the ratio from least to greatest would be A C B
Answer:
Sequence B, Sequence A, Sequence C
Step-by-step explanation:
Common ratio of a geometric sequence is the ratio of a term and its previous term of the sequence.
Thus, the common ratio of the sequence A: 160,40,10,2.5,...
[tex]r_1=\frac{40}{160}=\frac{1}{4}[/tex]
The common ratio of the sequence B: -21,63,-189,567,...
[tex]r_2=\frac{63}{-21}=-3[/tex]
The common ratio of the sequence C : 8,12,18,27,....
[tex]r_3=\frac{12}{8}=\frac{3}{2}[/tex]
Since, -3 < [tex]\frac{1}{4}[/tex] < [tex]\frac{3}{2}[/tex]
Thus,
[tex]r_2 < r_1 < r_3[/tex]
Hence, the order the sequences from least common ratio to the greatest common ratio is,
Sequence B, Sequence A, Sequence C
Bradley wanted a blue gumball and a green gumball from a vending machine. There were 15 blue gumballs, 12 yellow gumballs, 2 green gumballs, and 16 purple gumballs. How many times would you expect to get a blue gumball or green gumball if a gumball was taken out 250 times?
Answer: Bradley would expect 94 times to get a blue or green gumball.
Step-by-step explanation:
Since we have given that
Number of blue gumballs = 15
Number of yellow gumballs = 12
Number of green gumballs = 2
Number of purple gumballs = 16
Total number of all gumballs = 45
Probability of getting either a blue gumball or green gumball be
[tex]\frac{15}{45}+\frac{2}{45}=\frac{17}{45}[/tex]
So, Expectation of getting a blue gumball or green gumball if a gumball was taken out 250 times :
[tex]\frac{17}{45}\times 250=94.4[/tex]
Since we know that it must be less than 94.4.
So, the nearest smallest integer will be 94 times .
Hence, Bradley would expect 94 times to get a blue or green gumball.
Ashley has a balance of $4,000 on her credit card with an annual interest rate of 13%. To pay off the $4,000 in three years, Ashley will have to make a minimum payment of $134.78 per month. To pay off the $4,000 in five years, Ashley will have to make a minimum payment of $91.01 per month.
How much more interest will Ashley pay when the length of the loan changes from 3 years to 5 years?
A) $488.20
B) $608.52
C) $1,671.90
D) $5,460.60
The amount $180.00 is what percent greater than $135.00?
A.) 35%
B.) 133.33%
C.) 33.33%
D.) 25%
Answer:
Its Option C
Step-by-step explanation:
The difference is 180 - 135 = $45
So it is 45 * 100 / 135
= 33.33% greater
Answer: Its Option C
Step-by-step explanation:
Given the equation y = 3x − 4, what is the value of y when x = 4?
A) 2
B) 4
C) 8
D) 10
Answer:
C) 8
Step-by-step explanation:
y = 3x-4
Substitute x=4 into the equation
y = 3*4 -4
y = 12-4
y=8
Put the value of x = 4 to the equation y = 3x - 4:
[tex]y=3(4)-4=12-4=8[/tex]
Answer: C) 8A large container has a maximum capacity of 64 ounces The container is filled with 8 ounces less than its maximum capacity
The percentage of its capacity is the large container filled will be 87.5%.
What is mean by Percentage?
A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
To Calculate the percent of a number , divide the number by whole number and multiply by 100.
Given that;
A large container has a maximum capacity of 64 ounces.
And, The container is filled with 8 ounces less than its maximum capacity.
Now,
Calculate the percent of its capacity is the large container filled as;
Percent = (64 - 8) / 64 x 100
= 56/64 x 100
= 87.5%
Thus, The percentage of its capacity is the large container filled will be 87.5%.
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The complete question is this;
A large container has a maximum capacity of 64 ounces. The container is filled with 8 ounces less than its maximum capacity. To what percent of its capacity is the large container filled?
Waterworld properties to rewrite each expression as an expression that does not use parentheses (b + 3) + 6
Answer:
b+9
Step-by-step explanation:
(b + 3) + 6 = b + (3 + 6) = b + 9
In 1983 the composition of pennies in the United States was changed due, in part, to the rising cost of copper. Pennies minted after 1983 weigh 2.50 grams while the earlier copper pennies weigh 3.11 grams. a. A roll of pennies contains 50 pennies. If a particular roll of pennies weighs 138.42 grams, how many of the earlier copper pennies and how many of the after 1983 pennies does this roll contain? b. Suppose you measure a roll of pennies on a scale which only reads the weight to the nearest gram. The scale says that the roll of pennies weighs 131 grams. What can you conclude about the pennies in this roll? What if the roll weights 134 grams? Explain.
Answer:
Solution for (a)
Earlier Copper pennies are 22.
After 1983 pennies are 28.
Step-by-step explanation:
Pennies minted after 1983 weigh 2.50g
Earlier copper pennies weigh 3.11g
A roll of pennies contains 50 pennies.
A particular roll of pennies weighs 138.42g
Let the number of pennies minted after 1983 be x and;
Earlier copper pennies be 50 - x
2.50x + 3.11(50 - x) = 138.42
Opening the brackets gives;
2.5x + 155.5 - 3.11x = 138.42
Solving like terms together gives;
-0.61x = -17.08
Dividing through gives;
x = 28
So there are 28 after 1983 pennies and;
50 - 28 = 22 earlier pennies.
Say that you own property with a market price of $74,000. The state tax assessors have given it an assessed value of 48% of that amount. If your state’s property tax rate is 0.031, how much do you owe in property tax, to the nearest dollar? a. $1,101 b. $2,294 c. $35,520 d. $1,193
Answer:
A
Step-by-step explanation:
74,000 x .48 = 35520. 35520 is the amount of property you have to pay for.
35520 x 0.031 = 1,101.12. 1.101.12 is the amount you owe in property tax.
The amount owed in property tax to the nearest dollar is $1,101
What is the market price of a property?In real estate management, the market price is the price at which a buyer is willing to pay and which the seller is as agreed to receive at the present time.
From the parameters given:
The market price = $74000The state tax on the property = 48% = 0.48From the property, the required amount of property to be paid for is:
= $74000 × 0.48
= $35520
If the state property tax rate is 0.31, the amount owe in property tax is:
= $35520 × 0.031
= $1,101
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On Monday, Harry had 75\%75% as many toys as Teddy did. On Tuesday, after Harry acquired 3232 more toys and Teddy acquired 15\%15% more than he had on Monday, Harry had as many toys as Teddy did. How many toys did Harry have on Monday?
Answer:
60
Step-by-step explanation:
We can first define the variables as hh for the number of Harry's toys on Monday and tt for the number of Teddy's toys on Monday.
We know that on Monday, Harry had 75\%75% as many toys as Teddy, so we can write the following equation:
\qquad h=0.75th=0.75t
Hint #2
When we add 3232 toys to Harry's collection, we get h+32h+32. We can also make an adjustment to Teddy's collection, as he acquired 15\%15% more. We can represent that as 1.15t1.15t, as we should add 15\%15% to 100\%100% to get a percent increase.
Now let's make an equation for Tuesday:
\qquad h+32=1.15th+32=1.15t
Hint #3
We also know that h=0.75th=0.75t from the first equation, so we can substitute that in.
\qquad 0.75t + 32 = 1.15t0.75t+32=1.15t
Let's solve by first subtracting 0.75t0.75t from both sides.
\qquad 32 = 0.4t32=0.4t
We can then divide by 0.40.4 to solve for tt, and when we do that, we find that t=80t=80.
Hint #4
Since t=80t=80, we must substitute it into another equation to find hh (the number of toys Harry had on Monday). Let's pick the first equation.
\qquad h=0.75th=0.75t
\qquad h=0.75(80) = 60h=0.75(80)=60
Hint #5
Harry had 60 toys on Monday.
Which graph is the graph of y - 1 = 0 ?
Answer:
The answer is A because if you subtract the 1 you get y=1 and the line of A is at the point 1 on the y-axis
Step-by-step explanation:
write a statement that indicates that the triangles to each pair are congruent
Answer:
Triangles are congruent because all the corresponding sides and interior angles are congruent.
Step-by-step explanation:
In ΔWXY and ΔBCD
Given Sides are congruent:
[tex]WX \cong BC[/tex]
[tex]XY \cong CD[/tex]
[tex]YW \cong DB[/tex]
Also,
Angles are congruent i,e:
[tex]\angle W \cong \angle B[/tex]
[tex]\angle X \cong \angle C[/tex]
[tex]\angle Y \cong \angle D[/tex]
By congruence statement: If two sides in one triangle are congruent to two sides of a second triangle, and also if the included angles are congruent, then those triangles are congruent.
[tex]\triangle WXY \cong \triangle CBD[/tex]
Therefore, we can say the two triangles WXY and BCD are congruent because every corresponding side are of equal length and every corresponding angle has the same measure.
The given triangles WYX and BDC are congruent as all the sides as well as the angles are equal.
From the given figures,
[tex]WY=BD\\WX=BC\\YX=DC[/tex]
Also,
[tex]\angle{W}=\angle{B}\\\angle{Y}=\angle{D}\\\angle{X}=\angle{C}[/tex]
Hence, the triangles WYX and BDC are congruent to each other.
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For a certain manufacturer only 4/5 of the item produced are not defective. If 2,000 items are manufactured in a month, how many are not defective?
Answer:
1600 items should not be defective
Step-by-step explanation:
To determine the number of items that are not defective, we multiply the number of items we have by the probability that they are not defective.
Not defective items = items * probability
= 2000 * 4/5
1600
Answer:1600
Step-by-step explanation:
Question: 1. What is the value of x? Show your work to justify your answer. (2 points) 2. What is the value of the exterior angle? Show your work to justify your answer. (2 points)
Answer:
x=56 and the exterior angle is 116
Step-by-step explanation:
We will call the unknown angle in the triangle y. Angle y and the angle (2x +4) form a straight line so they make 180 degrees.
y + 2x+4 =180
Solve for y by subtracting 2x+4 from each side.
y + 2x+4 - (2x+4) =180 - (2x+4)
y = 180-2x-4
y = 176-2x
The three angles of a triangle add to 180 degrees
x+ y+ 60 = 180
x+ (176-2x)+60 = 180
Combine like terms
-x +236=180
Subtract 236 from each side
-x+236-236 = 180-236
-x = -56
Multiply each side by -1
-1*-x = -56*-1
x=56
The exterior angle is 2x+4. Substitute x=56 into the equation.
2(56)+4
112+4
116
Caroline ran 15 miles in 5 days. She ran the same distance each day. Write and solve an equation to determine the number of miles she ran each day
Answer:
15/5= x. x=3.
Step-by-step explanation:
Miles ran in total divided by days spent running equals miles ran each day.
find the square root of -36
[tex]i=\sqrt{-1}-\text{the imaginary number}\\\\\sqrt{-36}=\sqrt{(36)(-1)}=\sqrt{36}\cdot\sqrt{-1}=\boxed{6i}[/tex]
how do you solve -3y-8=25
PLEASE HELP!!
Identify the linear function graph.
A)
B)
C)
D)
Answer:
B
Step-by-step explanation:
linear is a straight line