The width of the paper in the smaller notebook is 4 1/4 inches.
When two shapes are similar, the ratio of their corresponding sides are equal, and their corresponding angles are equal.
For two notebooks in the shape of a rectangle, the ratio of their lengths must be equal to the ratio of their widths.
If one sheet of paper in a notebook is 8 1/2 inches by 11, and the pages of the smaller similar notebook are 5 1/2 inches long, then the width of the paper in the smaller notebook is
11 inches / 5 1/2 inches = 8 1/2 inches / width of smaller notebook
width of smaller notebook = 4 1/4 inches
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Last night, Luis read 75% more pages than Dayja, and Dayja read 75% more pages than Michael. If Dayja read 84 pages, how many pages did Luis, Dayja, and Michael read all together?
Answer:
Total pages read = 279 pages
Step-by-step explanation:
Let L, D, and M stand for the pages read by Luis, Dayja, and Michael, respectively.
We learn that:
L = 1.75D, [Luis read 75% more pages than Dayja]
D = 1.75M, and [Dayja read 75% more pages than Michael]
D = 84 [Dayja read 84 pages]
We want the sum of L, D, and M
Total pages = L + D + M
We have three equations and 3 unknowns. We should be able to find a solution by rearranging and substituting.
Total pages = L + D + M
We can substitute L=1.7D and rearrange D = 1.75 M to M = D/1.75
Total pages = L + D + M
Total pages = 1.7D + D + D/1.75
Total pages = D(1.7 + 1 + 1/1.75) [Isolate the D, for optional simplification]
Total pages = D(3.271)
We know D = 84, so:
Total pages = 84(3.271)
Total pages = 274.8
We'll round that to 275 pages.
Check:
L = 1.75D: L read 1.75*275 or 147 pages
D read 84 pages
D = 1.75M, or M = D/1.75; M read 84/1.75) or 48 pages
Total pages read = 147 + 84 + 48
Total pages read = 279 pages
matthew is thinking about applying for a credit card with a low interest rate. the loan application asks how much he owes on his mortgage and on his existing credit cards matthew used his calculator to figure out these two numbers and they are 2.4e5 and 1.25e4. how much money does matthew owe?(a) $232,500(b) $240,000(c) $252,500(d) $265,000
so:
[tex]240000+12500=252000[/tex]Answer:
(c) $252,500
A bank features a savings account that has an annual percentage rate of r=2.8% with interest. compounded quarterly. Benicio deposits $8,000 into the account.
Explanation
From the given question
We are given the formula to compute the amount that a sum of $8000 compounded quarterly will yield after time t at a rate of 2.8%
The formula is given by
[tex]A(t)=a(1+\frac{r}{k})^{kt}[/tex]Part A
[tex]\begin{gathered} a=initial\text{ deposit= \$8000} \\ \\ k=number\text{ of times compounded in a year = 4} \\ \\ r=2.8\text{ \% =0.028} \\ \\ \end{gathered}[/tex]part B
the amount in the account after 7 years will be
[tex]\begin{gathered} A(t)=8000(1+\frac{0.028}{4})^{4\times7} \\ \\ A(7)=\text{ \$}9725.57\text{ } \end{gathered}[/tex]The amount that will be in the account after 7 years will be $9725.57
Part C
APY is given by
In our case we have
[tex]\begin{gathered} APY=(1+\frac{r}{k})^k-1 \\ APY=\left(1+\frac{0.028}{4}\right)^4\:-1 \\ APY=1.02829-1 \\ APY=0.02829 \end{gathered}[/tex]Hence, we will have the APY as
[tex]\begin{gathered} APY=0.02829\times100\text{ \% } \\ APY=2.829\text{ \%} \end{gathered}[/tex]Hence, the APY is 2.829%
Suppose the commute times for employees of a large company follow anormal distribution. If the mean time is 24 minutes and the standarddeviation is 5 minutes, 95% of the employees will have a travel time within which range?
The empirical rule state that, for normally distributed data, almost all of the data fall within three standard deviations either side of the mean. Specifically,
-68% of data within 1 standard deviation.
-95% of data within 2 standard deviation
-99.7 of data within 3 standard deviation.
In our case the mean is
[tex]\mu=24[/tex]and the standard deviation is
[tex]\sigma=5[/tex]then, the empirical formula imply that
[tex]\begin{gathered} \mu-2\sigma=24-2\cdot5 \\ \mu-2\sigma=24-10 \\ \mu-2\sigma=14 \end{gathered}[/tex]and
[tex]\begin{gathered} \mu+2\sigma=24+2\cdot10 \\ \mu+2\sigma=24+10 \\ \mu+2\sigma=34 \end{gathered}[/tex]then, the answer is 14 minutes to 34 minutes
Answer:
D
Step-by-step explanation:
This is the only question I’m stuck on can someone explain and help me
Answer:
x = 58°
∠P = 58°
∠PQR = 64°
Step-by-step explanation:
If you add the two nonadjacent angles together they will equal the exterior angle. Setup up an equation using that info.
[tex]58 +x=2x[/tex]
Solve for x.
[tex]58 +x-x=2x-x\\58=x[/tex]
Since ∠P is the same as x, ∠P = 58°
To find ∠PQR, add ∠P and ∠R together and then subtract from 180°. You subtract from 180° because the sum of the three angles of a triangle equal 180°.
58 + 58 = 116
180 - 116 = 64°
∠PQR = 64°
is 12 an integer? Im getting confused answers
Answer:
Yes 12 is an Integer
Step-by-step explanation:
12 is a whole number that can be written without a fractional component, thus 12 is an integer.
kayla has a deck that measures 4 feet by 21 feet. she wants to increase each dimension by equal lengths so that the area is doubled. how much should she increase each dimension?
Answer:
Increase by 3.
Step-by-step explanation:
4 x 21 = 84
84 x 2 = 168
Begin to try numbers.
5 x 22 = 110
6 x 23 = 138
7 x 24 = 168
7 - 4 = 3
24 - 21 = 3
Increase each side by 3 ft. for a total dimension of 7 ft. x 24 ft.
The Busy Bee store bottles fresh jars of honey at a constant rate. In 2 hours, it bottles 20 jars, and in 5 hours, it bottles 50 jars of honey.
Determine the constant of proportionality.
(HELP THIS IS OVERDUE !!)
Answer:
9
Step-by-step explanation:
because in one hour it fills 18÷2 =9.
Answer: It's 10 because 20* Divided by 2 is 10
Step-by-step explanation:
Does anyone know how to write a linear equation to find the length and width of a perimeter? Ex...
Write a linear equation to represent the given problem and then solve the problem.
The perimeter of a rectangle is 150 cm. The length is 15 cm greater than the width. Find the dimensions.
The linear equation that represents the problem is 4w + 30 = 150.
The dimension(width and length) of the rectangle is 30 cm and 45 cm .
How to find the dimensions of a rectangle?A rectangle is a quadrilateral with 4 sides.
Opposite sides of a rectangle are equal to each other.
Opposite sides of a rectangle are parallel to each other.
Therefore,
perimeter of a rectangle = 2(l + w)
where
l = lengthw = widthHence, the perimeter of the rectangle is 150 cm. The length is 15cm greater than the width.
Therefore,
perimeter of rectangle = 150 cm
l = 15 + w
Hence,
150 = 2(15 + w + w)
150 = 2(15 + 2w)
150 = 30 + 4w
Therefore, the linear equation to represent the problem is 4w + 30 = 150.
Let's solve for the dimension of the rectangle.
4w + 30 = 150.
4w = 150 - 30
4w = 120
w = 120 / 4
w = 30 cm
L = 15 + 30 = 45 cm
Therefore,
length = 45 cm
width = 30 cm
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1 - -8= i am having trouble answering it
Answer:
Step-by-step explanation:
2 subtraction symbols equals a plus
so the answer is 9
Please help me solve this problem
The following table justifies the reasons of each step of the solution by stating the algebraic property that is used to get to each steps
What are algebraic equations?Algebraic equations are defined as mathematical statements in which two algebraic expressions are set equal to each other. An algebraic expression usually consists of a variable, a coefficients and a constants.
Statement Reason
4.5(8-x)+36=102-2.5(3x+24) Given
4.5(8-x)=66-2.5(3x+24) Subtracting 36 from the both sides
36-4.5x=66-7.5x-60 Opening the brackets on the both sides
36-4.5x=-7.5x+6 Subtracting the constants on RHS
36+3x=6 Adding -7.5x on the both sides
3x=-30 Subtracting 36 from the both sides.
x=-10 Dividing by 3 on the both sides.
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given l || m || n, find the value of x
Answer:
x = 10
Step-by-step explanation:
(5x + 3) and 53 are corresponding angles and are congruent , then
5x + 3 = 53 ( subtract 3 from both sides )
5x = 50 ( divide both sides by 5 )
x = 10
The value of 'x' is highlighted in the box
PLEASE HELP! this is probably easy, THANK YOU!
Answer:
The percent change in attendance from the 2014 to 2015 school year is a 11.5385% decrease, or 12% when rounded.
Make sure to mark as Brainliest if this is correct so others know that this is the correct answer.
Answer:
r u cheating or just need "HELP"
Step-by-step explanation:
Which pair of statements about the lengths of two sides of the triangle is true? 10 9 8 D (8,7) 7 л д) 4 3 2 1 X F(6, 1) 2 3 4 5 6 E (8.1) 8 9 10 1 7 O A. The side length between Dand Eis 7 units. The side length between Eand Fis 2 units. O B. The side length between D and Eis 6 units. The side length between E and Fis 2 units. O C. The side length between D and Eis 2 units. The side length between E and Fis 6 units. O D. The side length between D and Eis 8 units. The side length between Eand Fis 1 units.
Answer:
Choice B.
Explanation:
The side length is the distance between the vertices of the triangle given.
The segments shown below could form a triangle 6 5 8 true or false
It is true to state that segments 6 5 8 could form a triangle. Where AC = 6, CB =5 and BA = 8. See the explanation for the same below.
What is a Triangle?
A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. Triangle ABC denotes a triangle with vertices A, B, and C.
The total lengths of any two sides must always be larger than the length of the third side in order to make a triangle.
This is shown as follows:
6 + 5 = 11 > 8
5 + 8 = 13 > 6
8 + 6 = 14 > 5
Given that the side lengths meet the preceding criterion, a result, the supplied segments may be used to build a triangle.
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True, the segments 6, 5, and 8 form a triangle.
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
Let ABC is a triangle
AB=6
BC=5
CA=8
To form a triangle the sum of any two sides must be greater than the third side.
AB+BC>CA
6+5>8
11>8
BC+CA>AB
5+8>6
13>6
CA+AB>BC
8+6>5
14>5
It satisfies the condition for forming a triangle.
Hence the segments form a triangle.
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Stephanie has 5 pizzas. She shares 4-
of the pizzas with her friends. Estimate how much pizza Stephanie has left.
8
16
02/20
pizzas
O2 pizzas
O
01/P
pizzas
01 pizza
After subtraction we can see Stephanie has only 1 pizzas left.
What is subtraction?
The definition of subtraction is subtracting one number or amount from another. It is addition's opposite operation. Subtraction subtracts a number from another to find the difference, whereas addition adds or groups numbers to find the sum. The word "subtract" can also mean to compare two values to determine how many factors account for a value's difference from another. That is the most fundamental concept behind the term "difference" for the solution to a subtraction problem.
We are given that,
Stephanie has 5 pizzas, Also she shared 4 of the pizzas with her friends
Hence she is left with 5-4= 1 pizza
Hence Stephanie has left with 1 pizza
Therefore the correct option is option D)
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How many ways can four guests sit in a row of six chairs?
Answer:
360
Step-by-step explanation:
There are 6 spaces and 4 people.
_ _ _ _ _ _
The first person to choose a seat can choose any of the 6 seats.
The second person can choose any of the 5 remaining seats.
The third person can choose any of the 4 remaining seats.
The fourth person can choose any of the 3 remaining seats.
Now, we do 6 x 5 x 4 x 3 to figure out the total number of ways they can sit in the seats.
6 x 5 x 4 x 3 = 360 ways
What’s the answer plsss
Answer:
8.5 cm
Step-by-step explanation:
See attached worksheet.
Opposite 63 is ML (we are not after that)
Adjacent is MN
Hypotenuse is 18.8
Choose adjacent + Hypotenuse to find MN
AH - CAH, cos
Cos63 = A/18.8
x18. 8
18.8 x Cos63 = A
8.535.... = A
So, MN = 8.5cm
Ans: C
Hope this helps!
Question 5
The equation 2x² - 8x = 10 is rewritten in the form of 2(x-p)²+ q = 0. What is the value of q?
-18
2
-2
18
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.
For instance, the equation -2x²-8x = 10 consists of the two equations is rewritten in the form of 2(x-p)²+ q = 0. , which are separated by the 'equal' sign.
What are two illustrations of equations?Answer :q = -2
-2x²-8x = 10 (divide both sides by -2)
x² + 4x = -5 (Apply completing the square method)
x² + 4x + (4/2)²= -5 + (4/2)²
x² + 4x + 2²= -5 + 2² (reduce left hand side using a²+2ab+b² = (a+b)² )
(x+2)² = -5 +4
(x+2)² = -1
(x+2)² + 1 = 0 (multiply both sides by -2)
(-2)(x+2)² + 1 (-2) = 0
-2[x - (-2)]² + (-2) = 0 ---> compare this with -2(x-p)² + q = 0
We can see that p = 2 and q = -2
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Please help.
Is the answer ASA, SSS, AAS, or HL
Answer:
SSS
Step-by-step explanation:
We know the length of DE and JK are the same because as shown in the diagram, they are both equal to 15 cm. While we know that EF and KL are congruent because it is shown that both sides are 8 cm long. Even though we are not sure of the exact lengths of FD or LJ, we are aware that they are the same length sue to the ticks found on both sides on the triangles, indicating that they are both the same length.
If 8,x,y ,-4 are in A.p find x and y
Answer:
Step-by-step explanation:
firstly, 8+d=x and y+d= -4 where d is the common difference of the AP.
Also,
x+d=y;
therefore d=y-x;
so,
8+y-x=x (from the first equation)
=>8+y=2x
=>y=2x-8
Now from the second equation,
y+d= -4
(2x-8)+(y-x)= -4
=>x-8+2x-8= -4
=>3x=12
=>x=4
similarly,
y=2(4)-8
=>y=0
If 4x-y=-10 is a true equation, what would be the value of 6+4x-y
Answer:
-4
Step-by-step explanation:
6 + 4x-y = 6 + (4x-y) = 6 + (-10) = -4
30. Solve for x: 7^/10 = 2, approximate to 4 digitsa. 6.325 b. 3.256 c. 3.265 d. 3.652 e. 3.562
• Solution
[tex]7^{\frac{x}{10}}=2[/tex]
To solve for x, we take the logarithm of both sides.
[tex]\log 7^{\frac{x}{10}}=\log 2[/tex]Applying the law of logarithm to the equation above;
[tex]\log a^b=b\log a[/tex][tex]\begin{gathered} \log 7^{\frac{x}{10}}=\log 2 \\ \frac{x}{10}\log 7=\log 2 \\ \text{Dividing both sides by log 7;} \\ \frac{x}{10}=\frac{\log 2}{\log 7} \\ \frac{x}{10}=\frac{0.3010}{0.8451} \\ \frac{x}{10}=0.3562 \\ \text{Cross multiplying the equation;} \\ x=0.3562\times10 \\ x=3.562 \end{gathered}[/tex]Therefore, the approximate value of x is 3.562
The correct option is E.
Select all the unique triangles that can be drawn to only have angle measures 40° and 100° and side length 3.
ΔABC; AB = 3, ∠CBA = 100°, ∠CAB = 40°
ΔABC; AB = 3, ∠ABC = 100°, ∠BCA = 40°
Given,
Select all the unique triangles that can be drawn to only have angle measures 40° and 100° and side length 3.
What are unique triangles?
Unique triangles are triangles that are different based on their configuration, which derives from the positioning of the given parameters to correspond with different congruency requirement.
The conditions for the congruency of two triangles are;
SSS: The Side-Side-Side rule; two triangles are congruent if all three sides of one triangle are congruent to the three sides of the other triangle
SAS: The Side-Angle-Side rule; two triangles are congruent if two sides and the included angle of one are congruent to two sides and an included angle in the other triangle
ASA: The Angle-Side-Angle rule; two triangles are congruent if two angles and the included side of one triangle are congruent to two angles and an included side of the other triangle
SAA: The Side-Angle-Angle rule; Two triangles are congruent if two angles and an a non included side of one triangle are congruent to two angles and the non included side of the other triangle.
The configuration of the unique triangles can therefore, be ASA and SAA, which gives the triangles;
ΔABC; AB = 3, ∠CBA = 100°, ∠CAB = 40°
ΔABC; AB = 3, ∠ABC = 100°, ∠BCA = 40°
Please see attached drawings of the two unique triangles
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Simplify nine square root of two minus three square root of seven plus square root of eight minus square root of twenty eight. eleven square root of two minus five square root of seven eleven square root of four minus five square root of fourteen six square root of five six square root of nine
Squares are the numbers that are produced when a value is multiplied by itself.
If expression be [tex]$9 \sqrt{2}-3 \sqrt{7}+\sqrt{8}-\sqrt{28}$[/tex] then the value exists [tex]$11 \sqrt{2}-5 \sqrt{7}$[/tex].
What is meant by square root?The radical symbol for the number's root is "√" in this instance. The square of the positive number is represented by multiplying it by itself.
Squares are the numbers that are produced when a value is multiplied by itself. In contrast, a number's square root exists a value that, when multiplied by itself, returns the original value.
The original number can be attained by multiplying the square root of an integer by itself.
Only a perfect square number can have a perfect square root. Even perfect squares have an even square root. An odd perfect square will contain an odd square root. A perfect square cannot be negative and hence the square root of a negative number exists not defined.
Let the expression be [tex]$9 \sqrt{2}-3 \sqrt{7}+\sqrt{8}-\sqrt{28}$[/tex]
Now, [tex]$\sqrt{8}=\sqrt{2 \times 2 \times 2}=2 \sqrt{2}$[/tex]
[tex]$\sqrt{28}=\sqrt{2 \times 2 \times 7}=2 \sqrt{7}$[/tex]
therefore [tex]9 \sqrt{2}-3 \sqrt{7}+\sqrt{8}-\sqrt{28}$[/tex]
simplifying the given expression, we get
[tex]$=9 \sqrt{2}-3 \sqrt{7}+2 \sqrt{2}-2 \sqrt{7}$[/tex]
[tex]$=9 \sqrt{2}+2 \sqrt{2}-3 \sqrt{7}-2 \sqrt{7}$[/tex]
[tex]$=11 \sqrt{2}-5 \sqrt{7}$[/tex]
Therefore, the correct answer is option a) [tex]$11 \sqrt{2}-5 \sqrt{7}$[/tex]
The complete question is:
Simplify [tex]$9 \sqrt{2}-3 \sqrt{7}+\sqrt{8}-\sqrt{28}$[/tex]
a) [tex]$11 \sqrt{2}-5 \sqrt{7}$[/tex]
b) [tex]$11 \sqrt{4}-5 \sqrt{14}$[/tex]
c) [tex]$6 \sqrt{5}$[/tex]
d) [tex]$6 \sqrt{9}$[/tex]
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Multiply and write in standard form: 10x + 3)(2x - 1) Show all work
Explanation
[tex](10x+3)(2x+1)[/tex]Step 1
apply distributive property
[tex]\begin{gathered} (10x+3)(2x+1)=(10x\cdot2x)+(10x\cdot1)+(3\cdot2x)+(3\cdot1) \\ (10x+3)(2x+1)=20x^2+10x+6x+3 \end{gathered}[/tex]Step 2
add similar terms and order
[tex]\begin{gathered} (10x+3)(2x+1)=20x^2+10x+6x+3 \\ (10x+3)(2x+1)=20x^2+16x+3 \\ \text{the standard form is} \\ ax^2+bx+c,so \\ ax^2+bx+c\Rightarrow20x^2+16x+3 \end{gathered}[/tex]so, the answer is
[tex]20x^2+16x+3[/tex]I hope this helps you
Triangle XYZ with vertices X(-8, 3), Y(-6, 5), and Z(-5, -2): x = -4
Answer:
X' = (-12,3)
Y' = (-10,5)
Z' = (-9,-2)
Explaination:
Please check image
Based off the x = -4 , I think that means that our x axis is no longer x = 0 but on the x = -4 line
Ex;
if point X is 8 units to the left of x=0, now point X' should be 8 units to the left of x=-4 making point X' = (-12,3)
Given: angle CDE congruent to angle CED,
Angle A = angle B
Prove: DE || AB
Please explain the statement and reasoning
Ex: AB is congruent (the sign) to DE. Given
Ill reward brainliest to the one who explains it best ty
1) [tex]\angle CDE \cong \angle CED, \angle A \cong \angle B[/tex] (given)
2) [tex]m\angle CDE=m\angle CED, m\angle A=m\angle B[/tex] (definition of congruent angles)
3) [tex]m\angle C+m\angle CDE+m\angle CED=180^{\circ}, m\angle C+m\angle A+m\angle B=180^{\circ}[/tex] (sum of angles in a triangle)
4) [tex]m\angle C+2m\angle CDE=180^{\circ}, m\angle C+2m\angle A=180^{\circ}[/tex] (substitution)
5) [tex]m\angle C=180^{\circ}-2m \angle CDE, m\angle C=180^{\circ}-2m\angle A[/tex] (subtraction)
6) [tex]180^{\circ}-2m \angle CDE=180^{\circ}-2m \angle A[/tex] (transitive)
7) [tex]-2m\angle CDE=-2m\angle A[/tex] (subtraction)
8) [tex]m\angle CDE=m\angle A[/tex] (division)
9) [tex]\angle CDE \cong \angle A[/tex] (definition of congruent angles)
10) [tex]\overline{DE} \parallel \overline{AB}[/tex] (converse of corresponding angles theorem)
What’s the area ? 50 points
Answer:
The area of the figure is 325.17 ft²===============================
The area of the given shape can be found as a sum of three simpler shapes:
Triangle, rectangle and semi-circle.The semi-circle has the radius of 9 ft, its area is:
A = πr²/2 = 3.14*9²/2 = 127.17 ft²The rectangle has dimensions of 9 ft and 26 - 9 = 17 ft, its area:
A = lw = 9*17 = 153 ft²The triangle has bas of 9 ft and height 26 - 9 - 7 = 10 ft, its area is:
A = bh/2 = 9*10/2 = 45 ft²Area of the shape is:
A = 127.17 + 153 + 45 = 325.17 ft²Select the correct answer. Consider the graph of f(x) given below. The function g(x) is a transformation of f(x). If g(x) has a y-intercept of -2, which of the following functions could represent g(x)? A. g(x) = f(x - 5) B. g(x) = f(x) - 2 C. g(x) = f(x) - 5 D. g(x) = f(x + 2)
PLEASE OFFER ME YOUR ANSWER, I ASK OF YOU...PLS
The function that could represent g(x) is (c) g(x) = f(x) - 5
How to determine the function g(x)?The figure of the graph that completes the question is added as an attachment
From the attached graph, we have the equation of the function to be
y = f(x)
Also, the graph of the function f(x) has its intercept to be
y-intercept of f(x) = 3
From the question, we have
y-intercept of g(x) = -2
Subtract the intercepts
Difference = y-intercept of g(x) - y-intercept of f(x)
So, we have
Difference = -2 - 3
Evaluate
Difference = -5
The function g(x) is then represented as
g(x) = f(x) + Difference
So, we have
g(x) = f(x) - 5
Hence, the function g(x) is g(x) = f(x) - 5
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