Tim enlarged a picture with a width of 5.5 inches and a length of 8 inches by a scale factor of 3. What are the dimensions of the enlargement?
a. width: 24 in.; length: 16.5 in.b. width: 16.5 in.; length: 24 in.c. width: 14.5 in.; length: 22 in.d. width: 19.5 in.; length: 25 in.
Answer:
Option b. width = 16.5 inches and length = 24 inches
Step-by-step explanation:
Tim enlarged a picture wit a width of 5.5 inches and a length of 8 inches.
He enlarged the picture by a scale factor of 3.
We have to find the new dimensions of the picture.
Since, New dimension of the picture = Scale factor × dimensions before enlargement
So new width = 3×5.5 = 16.5 inches
new length = 3×8 = 24 inches
Therefore, option b. is the answer.
A lawn mower manufacturer incurs a total of $34,816 in overhead costs and $388 per lawn mower in production costs. How many lawn mowers were manufactured if the average cost of production is $660?
Answer:
128 lawn mowers
Step-by-step explanation:
Given,
The overhead cost = $ 34,816,
The cost for one lawn mower = $ 388,
Let x be the number of lawn mowers manufactured,
So, the total cost of x lawn mowers = 34816 + 388x,
Now, if the average cost of x mowers = $ 660,
So, the total cost = 660x
[tex]\implies 660x = 34816 + 388x[/tex]
[tex]660x - 388x = 34816[/tex]
[tex]272x= 34816[/tex]
[tex]\implies x = \frac{34816}{272}=128[/tex]
Hence, 128 lawn mowers were manufactured.
eight times the sum of a and b
The question concerns a basic algebraic expression 'eight times the sum of a and b' which is represented as 8(a + b). The expression emphasizes the operation order: sum first, then multiply, which results in a value eight times greater than the original sum.
Explanation:The question 'eight times the sum of a and b' is a mathematical expression that can be represented as 8(a + b). This expression means you first add the numbers 'a' and 'b' and then multiply their sum by eight. The result you get after the multiplication will be eight times greater than the original sum of 'a' and 'b'. For instance, if 'a' is 2 and 'b' is 3, their sum is 5, and when this is multiplied by eight, it becomes 40, which is the desired expression's value.
To understand this concept further, we can refer to the exponentiation rule mentioned, which states that (xa)b = xa.b. Although this is a different type of operation—exponentiation—it demonstrates a similar principle of first performing the operation inside the parentheses and then applying the outside operation.
Finally, when performing algebraic operations, it's essential to remember that whatever you do to one side of the equation, you should do to the other side to maintain balance. This is a fundamental principle in algebra that helps to solve equations, such as the example provided showing how to isolate 'a' by subtracting 'x' from both sides of the equation a b.
Find the lateral area for the prism. L.A. =
Find the total area for the prism. T.A. =
Answer:
Part 1) [tex]LA=(80+16\sqrt{13})\ in^{2}[/tex]
Part 2) [tex]TA=(104+16\sqrt{13})\ in^{2}[/tex]
Step-by-step explanation:
Part 1) Find the lateral area of the prism
we know that
The lateral area of the prism is equal to
[tex]LA=Ph[/tex]
where
P is the perimeter of the base
h is the height of the prism
Applying the Pythagoras Theorem
Find the hypotenuse of the triangle
[tex]c^{2}=4^{2}+6^{2}\\ \\c^{2}=52\\ \\c=2\sqrt{13}\ in[/tex]
Find the perimeter of triangle
[tex]P=4+6+2\sqrt{13}=(10+2\sqrt{13})\ in[/tex]
Find the lateral area
[tex]LA=Ph[/tex]
we have
[tex]P=(10+2\sqrt{13})\ in[/tex]
[tex]h=8\ in[/tex]
substitutes
[tex]LA=(10+2\sqrt{13})*8=(80+16\sqrt{13})\ in^{2}[/tex]
Part 2) Find the total area of the prism
we know that
The total area of the prism is equal to
[tex]TA=LA+2B[/tex]
where
LA is the lateral area of the prism
B is the area of the base of the prism
Find the area of the base B
The area of the base is equal to the area of the triangle
[tex]B=\frac{1}{2}bh[/tex]
substitute
[tex]B=\frac{1}{2}(6)(4)=12\ in^{2}[/tex]
Find the total area of the prism
[tex]TA=LA+2B[/tex]
we have
[tex]B=12\ in^{2}[/tex]
[tex]LA=(80+16\sqrt{13})\ in^{2}[/tex]
substitute
[tex]TA=(80+16\sqrt{13})+2(12)=(104+16\sqrt{13})\ in^{2}[/tex]
Factor the polynomial.
4x7+32x+5-24x^4
A. 4x^4(x^3+8x-6)
B. 2x^4(2x^3+16x-12)
C. 2x^4(x3+8x-6)
D. 4x^4(2x^3+16x-12)
HELP!!!!!!! I GIVE BRAINLEST AND THANKS!!!!!! + 5 POINTS!!!!
angle ABD and angle DBC are supplementary. Find the value of x.
A. 6
B. 8
C. 4
D. 10
According to the text, which is not a main component of drawing?
Perspective
Vanishing point
Horizon
If a train travels one mile (5,280 feet) while climbing a hill at an angle of five degrees, approximately how many vertical feet has the train climbed?
to calculate the vertical height multiply the hypotenuse ( 5280) by the sin of the angle (5)
5280 x sin(5) = 460.1823
round off to 460 feet
WILL GIVE BRAINLIST!!!!!!!!!!!!!! A group of students were surveyed to find out if they like working as a camp counselor and/or as a lifeguard during summer break. The results of the survey are shown below:
32 students like working as a camp counselor
8 students like working as a camp counselor but do not like working as a lifeguard
29 students like working as a lifeguard
8 students do not like working as a lifeguard or a camp counselor
Four students created the tables below to represent the data. CC represents camp counselor and LG represents lifeguard.
Which student's table is correct?
Answer:
I think Table C - Corralle
Answer:
c
Step-by-step explanation:
Kenya plans to make a down payment plus monthly payments in order to buy a motorcycle. At one dealer she would pay $2,500 down and $150 each month. At another dealer, she would pay $3,000 down and $125 each month. After how many months would the total amount paid be the same for both dealers? What would that amount be?
Let us say that the total amount paid in the first dealer is P1 and the total amount paid to the second dealer is P2. So that:
P1 = 2500 + 150 t
P2 = 3000 + 125 t
Where t is the total number of months
Now we are asked when the total amount paid would be equal for the two dealers, this means P1 = P2, therefore equating the two:
2500 + 150 t = 3000 + 125 t
25 t = 500
t = 20 months
Therefore the total amount paid for both dealers would be equal after 20 months.
A gas station is 12 kilometers away. How far is the gas station in miles? Use the following conversion: 1 mile is 1.6 kilometers.
Find the probability of drawing a king from a standard deck of cards and then drawing a queen after the first card is replaced in the deck. None of the above 1/26 1/13 1/2704 2/13
52 cards in a deck
4 kings
4 queens
King = 4/52 reduces to 1/13
Queen = 4/52 reduces to 1/13
1/13 *1/13 = 1/169
so none of the above
Four times the sum of a number and 15 is at least 120. Find all possible solutions for x
12.5% of what is 130?
How could you find the y-coordinate of the midpoint of a vertical line segment with endpoints at (0,0) and (0,-12)
What numbesr can be multiplied and added to equal the same number?
2
2x2 = 4
2+2 =4
0
0x0=0
0+0=0
Find the simple interest paid for 8 years on a $850 loan at 7.5% per year.
The simple interest paid for 8 years on a $850 loan at a 7.5% annual interest rate is $510.
To calculate simple interest, you can use the formula:
Simple Interest (SI) = Principal (P) × Rate (R) × Time (T)
Where:
- Principal (P) is the initial amount of the loan.
- Rate (R) is the annual interest rate (in decimal form).
- Time (T) is the number of years.
In this case:
- Principal (P) = $850
- Rate (R) = 7.5% = 0.075 (decimal form)
- Time (T) = 8 years
Now, plug these values into the formula:
SI = $850 × 0.075 × 8
SI = $510
The simple interest paid for 8 years on a $850 loan at a 7.5% annual interest rate is $510.
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Find the domain of the following piecewise function
Chase makes 2 gallons of soup for a dinner party. He serves 10 cups of soup to his guests. How many cups of soup will be have left over?
For an angle θ with the point (–20, –21) on its terminating side, what is the value of cosine?
Answer:
-20/29
Step-by-step explanation:
Read the following statement: If the sum of two angles is 90°, then the angles are complementary. The hypothesis of the statement is:
there are two angles.
the sum of two angles is 90°.
the angles are complementary.
Angles are complementary if their sum is 90°.
The hypothesis in the given mathematical conditional statement 'If the sum of two angles is 90°, then the angles are complementary.' is 'the sum of two angles is 90°'.
Explanation:In a conditional statement in mathematics, the 'if' part of the statement is called the hypothesis and the 'then' part is termed the conclusion. Given the statement 'If the sum of two angles is 90°, then the angles are complementary.', the hypothesis of this statement is 'the sum of two angles is 90°'.
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In a conditional statement, the hypothesis is the condition that needs to be met. In this case, the hypothesis of the statement 'If the sum of two angles is 90°, then the angles are complementary,' is 'the sum of two angles is 90°.'
Explanation:In the context of the given conditional statement, 'If the sum of two angles is 90°, then the angles are complementary,' the hypothesis refers to the clause immediately after 'if.' This indicates the condition that needs to be fulfilled for the conclusion to be considered valid. Therefore, the hypothesis for this statement is 'the sum of two angles is 90°'.
After the 'if,' the hypothesis is given, and after the 'then,' you find the conclusion. The conclusion in this case is 'the angles are complementary.'
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the answer to number 3
How to factor 2p^4+9p^3-18p^2
what is the value of the fourth term in a geometric sequence for which a1=15 and r=1/3
express your answer as a fraction
Answer: The required fourth term in the given geometric sequence is [tex]\dfrac{5}{9}.[/tex]
Step-by-step explanation: We are given to find the fourth term of a geometric sequence with the following first term and common ratio :
[tex]a=15,~~r=\dfrac{1}{3}.[/tex]
We know that
the nth term of a geometric sequence with first term a and common ratio r is given by
[tex]a_n=ar^{n-1}.[/tex]
Therefore, the forth term of the given geometric sequence is
[tex]a_4=ar^{4-1}=ar^3=15\times\left(\dfrac{1}{3}\right)^3=15\times\dfrac{1}{27}=\dfrac{5}{9}.[/tex]
Thus, the required fourth term in the given geometric sequence is [tex]\dfrac{5}{9}.[/tex]
Sherita’s club is selling grapefruit to raise money. For every box they sell, they get $1.35 profit. They have sold 84 boxes already. How many more boxes must they sell to raise 270 dollars
If h(x)=6-x, what is the value of (h o h)(10)
A circle of radius 1 centered at (4, 0) is rotated about the y-axis.
1) Draw a picture of the three-dimensional shape that is produced when the circle is rotated about the y-axis.
2) In two or more complete sentences, describe the three-dimensional shape.
please help and thank you.
Perform Gauss-Jordan elimination on the augmented matrix shown.
Could someone please help me figure this out.
14÷420 long division