Answer:
14 inches by 18 inches
Step-by-step explanation:
Old rectangular monitor screen:
Width = x in
Length = x + 4 in
Area [tex]=x(x+4)\ in^2[/tex]
New rectangular monitor screen:
Width = x - 1 in
Length = 2(x + 4) in
Area [tex]=(x-1)(2(x+4))=2(x-1)(x+4)\ in^2[/tex]
This area would be increased by [tex]216\ in^2,[/tex] so the area would be equal to [tex]x(x+4)+216\ in^2[/tex]. Hence,
[tex]2(x-1)(x+4)=x(x+4)+216\\ \\2(x^2+4x-x-4)=x^2+4x+216\\ \\2x^2+6x-8-x^2-4x-216=0\\ \\x^2+2x-224=0\\ \\D=2^2-4\cdot (-224)=4+896=900\\ \\x_{1,2}=\dfrac{-2\pm \sqrt{900}}{2}=\dfrac{-2\pm 30}{2}=-16,\ 14[/tex]
The width cannot be negative, so
Width = 14 in
Length = 14 + 4 = 18 in
In triangle VWX, VW = 4.5 inches, WX = 5.9 inches, Measure of angle W = 28 degrees, and Measure of angle X = 47 degrees. If Triangle P Q R is congruent to triangle W V X, which statement is true?
a.QR = 4.5 cm
b.QR = 5.9 cm
c.Measure of angle R = 28 degrees
d.Measure of angle R = 47 degrees
The true statement about triangle is: b. QR = 5.9 cm.
To understand what it means for two triangles to be congruent. When two triangles are congruent (△PQR ≌ △WVX), all corresponding sides and angles are equal.
Given:
VW = 4.5 inchesWX = 5.9 inches∠W = 28°∠X = 47°For the triangles to be congruent, the corresponding sides and angles must be equal. Let's match the corresponding parts:
QR corresponds to WXPQ corresponds to VWm∠R corresponds to m∠Wm∠Q corresponds to m∠XGiven this correspondence:
QR must be equal to WX, so QR = 5.9 inches (Option b).
m∠R must be equal to m∠W, so m∠R = 28° (Option c).
m∠Q must be equal to m∠X, so m∠Q = 47° (Option d).
However, m∠R and m∠Q cannot both be correct choices simultaneously; only one can be correct because they refer to the same angle in each corresponding pair QR = 5.9 inches is the correct choice considering the triangle sides.
Complete question
In triangle VWX, VW=4.5 inches, WX=5.9 incheß, m∠ W=28° , and m∠ X=47°. If △ PQR≌ △ WVX , which statement is true?
a. QR=4.5cm
b. QR=5.9cm
c. m∠ R=28°
d. m∠ R=47°
Which of the following must be true in order for SAND to be in a rhombus? Select all that apply
a) Consecutive sides must be congruent, for SAND to be in a rhombus
For the word "SAND" to form a rhombus, certain conditions must be met based on the properties of a rhombus:
a) Consecutive sides must be congruent: True. In a rhombus, all sides are congruent, so consecutive sides must also be congruent.
b) Diagonals do not bisect the angles: False. In a rhombus, the diagonals bisect the angles. This is a property of rhombuses.
c) All interior angles add up to 360: False. In a rhombus, all interior angles are equal, but their sum is not necessarily 360 degrees. However, the sum of all interior angles in any quadrilateral (including a rhombus) is indeed 360 degrees.
Therefore, the correct statement is:
a) Consecutive sides must be congruent
12abx square - (9a square - 8b square)x - 6ab =0
The value of x is [tex]\frac{3a}{4b}[/tex] and [tex]-\frac{2b}{3a}[/tex]
Explanation:
The expression is [tex]12abx^{2} -(9a^{2} -8b^{2} )x-6ab=0[/tex]
Multiplying the term x withing the bracket, we get,
[tex]12abx^{2} -9a^{2} x+8b^{2} x-6ab=0[/tex]
Grouping the terms, we have,
[tex](12abx^{2} -9a^{2} x)+(8b^{2} x-6ab)=0[/tex]
Taking out the common terms in each bracket, we get,
[tex]3ax(4bx -3a)+2b(4bx-3a)=0[/tex]
Simplifying, we get,
[tex](3ax+2b)(4bx -3a)=0[/tex]
Equating each term to zero, we get,
[tex]\begin{aligned}3 a x+2 b &=0 \\3 a x &=-2 b \\x &=-\frac{2 b}{3 a}\end{aligned}[/tex] and [tex]\begin{aligned}4 b x-3 a &=0 \\4 b x &=3 a \\x &=\frac{3 a}{4 b}\end{aligned}[/tex]
Hence, the values of x is [tex]\frac{3a}{4b}[/tex] and [tex]-\frac{2b}{3a}[/tex]
(12 r) (r 6) m=2
PLEASE HELP AND SHOW YOUR WORK!!!!
Answer:
seems like you need to learn how to do your own work.
Step-by-step explanation:
Ask instructor for help or go back to the book
What two numbers multiplies to -51 and adds to -14?
Answer: -17 and 3
Step-by-step explanation:
First try and find numbers that are divisible by -51 and see if they work. Then you'll find -17, leading to you multiplying -17 with 3, then you get -51, and if you add them, then you get -14.
You roll a pair of fair dice. Classify the probability for each of the outcomes as Impossible, Unlikely, Likely, or Certain.
Answer:
THE DIFFERENCE OF THE NUMBERS IS 6~ likely
THE SUM ON EACH DIE IS 5~ unlikely
THE NUMBER ON EACH DIE IS A WHOLE NUMBER~ Certain
THE NUMBER ON EACH DIE IS LESS THAN 6~ likely
THE SUM OF THE NUMBERS IS 14 OR GREATER~ impossible
A circuit board manufacturer can produce 2000 board per hour. How many days will it take to produce 16500 if the company has a 10 hour work shift
Answer:
B. Less than a day
Step-by-step explanation:
From the question, the circuit board manufacturer produces 2000 board per hour.
Let x be the number of hours it will take to produce 16500 boards .
That’s
2000 boards = 1 hour
16500 boards = x hour
Cross multiply
xhour x 2000 = 1 x 16500
x hour = 16500/2000
x hour = 8.25 hours
8.25 hours is less than a day
Find the area of the figure.( sides meet at right angles)
Rectangle ABCD is graphed in the coordinate plane. The following are the vertices of the rectangle: A(-4, -2), B(-2, -2), C(-2, 7)C(−2,7)C, D(-4, 7
What is the area of rectangle ABCD?
Answer:
The area of rectangle ABCD is [tex]18\ units^2[/tex]
Step-by-step explanation:
Plot the figure to better understand the problem
we have the vertices
A(-4, -2), B(-2, -2), C(-2, 7), D(-4, 7)
see the attached figure
The area of the rectangle is equal to
[tex]A=LW[/tex]
where
L is the length
W is the width
In this problem we have
[tex]L=BC=7-(-2)=9\ units[/tex] ---> difference of the y-coordinates
[tex]W=AB=-2-(-4)=2\ units[/tex] ---> difference of the x-coordinates
substitute
[tex]A=(9)(2)=18\ units^2[/tex]
Final answer:
The area of rectangle ABCD is calculated as 18 square units by finding the product of its width (2 units) and height (9 units).
Explanation:
The area of rectangle ABCD with vertices A(-4, -2), B(-2, -2), C(-2, 7), and D(-4, 7) can be calculated by finding the lengths of the sides AB and BC. The length of AB (width) is the difference in the x-coordinates of A and B, which is |-2 - (-4)| = 2.
The length of BC (height) is the difference in the y-coordinates of B and C, which is |7 - (-2)| = 9. Therefore, the area of rectangle ABCD is the product of the width and height, which is 2 * 9 = 18 square units.
Question 7 Aya and Kendra want to estimate the height of a tree. On a sunny day, Aya measures Kendra's shadow as 3 meters long, and Kendra measures the tree's shadow as 15 meters long. Kendra is 1.5 meters tall. How tall is the tree?
A.7.5 meters
B.22.5 meters
C.30 meters
D.45 meters
Which number is a common factor of 32, 48. and 80?
12
10
8
9
Answer:
8 because 32÷8=4,48÷8=6,80÷8=10
Use the linear combination method to solve this system of equations. What is the value of 3x+7y=3 X-7y=1
Answer:
look at the picture shown
Answer:
c
Step-by-step explanation:
Construct a triangle ABC where BC =4cm ,B=60° and AB+AC=6cm
Answer:
Below is the step-by-step explanation.
Step-by-step explanation:
To determine:
Construct a triangle ABC
Information Fetching and Information Steps:
From the given data,
[tex]BC\:=\:4\:cm[/tex][tex]B=60^{\circ }[/tex][tex]AB+AC=6\:cm[/tex]Procedure:
First draw a line segment [tex]BC\:=\:4\:cm[/tex]Then construct angle of [tex]m[/tex] ∠ [tex]60^{0}[/tex] at [tex]B[/tex] on [tex]BC[/tex].Taking [tex]B[/tex] as center with [tex]6\:cm[/tex] radius, draw an arc which cuts the ray of [tex]m[/tex] ∠ [tex]60^{0}[/tex] at [tex]X[/tex].Then Join [tex]X[/tex] and [tex]C[/tex].The draw a perpendicular bisector of [tex]XC[/tex].Wherever this perpendicular bisector intersect [tex]BX[/tex], name that point as [tex]A[/tex]Join [tex]A[/tex] and [tex]C[/tex].Thus, ∆ [tex]ABC[/tex] will be a required triangle.
Keywords: triangle, perpendicular bisector, angle
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Solve this system using any method (substition elimination) Thank you!!!
x - y = -3
-4x + y = -18
Answer:
look at the picture shown
What’s 2percent of 300
Answer:
6
Step-by-step explanation:
2%=0.02
0.02*300=6
An image point of a transformation has coordinates Y'(2, -4). If the pre-image point had coordinates Y(6, -12), what was the transformation and scale factor?
reflection with scale factor 3
reflection with scale factor 1/3
dilation with scale factor 3
dilation with scale factor 1/3
Answer:
Therefore the correct answer is the fourth one d.) dilation with scale factor 1/3
Step-by-step explanation:
i) the pre-image co-ordinates is Y(6, -12)
ii) the coordinates of the image is Y' (2, -4)
iii) therefore we can clearly see that if we divide the coordinates of the pre-image (6,-12) by 3 then we get the coordinates of the image(2,4).
Therefore this is a dilation with scale factor of 1/3.
Therefore the correct answer is the fourth one d.) dilation with scale factor 1/3
Final answer:
The transformation from the pre-image point Y(6, -12) to the image point Y'(2, -4) is a dilation with a scale factor of 1/3.
Explanation:
Given an image point Y'(2, -4) of a transformation and the pre-image point Y(6, -12), we can determine the type of transformation and the scale factor. The transformation is a type of change that affects the position, size, or shape of a figure. To find out the type of transformation and the scale factor, we compare coordinates.
Since the x-coordinate changed from 6 to 2, it has been reduced by a factor of 3 (6 divided by 3 equals 2). The y-coordinate changed from -12 to -4, which also has been reduced by a factor of 3 (-12 divided by 3 equals -4). This consistent reduction indicates that the transformation is a dilation. The objects are shrunk uniformly in both dimensions by the scale factor.
The correct answer is therefore dilation with scale factor 1/3.
Ben bowled 121 and 184 in his first two games. What must he bowl in his third game to have an average of at least 170?
Answer:
205
Step-by-step explanation:
Were gonna start by writing an equation (121+184+x)/3=170 because were adding a 3rd value to the average and x is going to be our value that were looking for. If you solve that, you get 205. Hope this helps.
For Ben to have an average of at least 170 in his third game, he must bowl a score of 205.
Explanation:To find out what Ben must bowl in his third game to have an average of at least 170, we can use the formula for average: average = total score/number of games.
In this case, Ben has played two games and wants to have an average of 170. So we can set up the equation: 170 = (121 + 184 + x) / 3, where x represents his score in the third game.
To solve for x, we can multiply both sides of the equation by 3 to get rid of the fraction: 510 = 121 + 184 + x.
Then, we can combine the numbers on the right side: 510 = 305 + x.
Finally, subtracting 305 from both sides gives us: 205 = x.
Therefore, Ben must bowl a score of 205 in his third game to have an average of at least 170.
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Please answer the question in the photograph
What’s 6 1/4 minus 2 3/4
Answer: 3.5
Step-by-step explanation:
yes
Please help!!!!
a + b = 10
a - b = 2
Solve the system of equations.
A) a = 5, b = 5
B) a = 2, b = 8
C) a = 6, b = 4
D) a = 3, b = 7
E) a = 12, b = -2
Answer:
C) a = 6, b = 4
Step-by-step explanation:
6 + 4 = 10
6 - 4 = 2
To solve the system, we first add both equations to find 'a = 6'. Then, substitute 'a' in one of the original equations to get 'b = 4'. The solution is 'a = 6' and 'b = 4', corresponding to answer choice C).
Explanation:To solve the system of equations:
a + b = 10a - b = 2We can add the two equations to eliminate the variable b. By adding them, we get:
2a = 12
Divide both sides of the equation by 2:
a = 6
With the value of a known, substitute a = 6 into either of the original equations. For example, substituting it into the first equation:
a + b = 10
6 + b = 10
b = 10 - 6
b = 4
Therefore, the solution to the system of equations is a = 6 and b = 4, which corresponds to answer choice C).
2 with an exponent of -2
Answer:
0.25
Step-by-step explanation:
2^-2=0.25
1. Veronica cut a
triangular piece of
cookie cake with side
lengths that measure
3.6 cm, 6 cm and 4.8
cm.
The question is about calculating the center of mass for a triangular sandwich with a semicircular bite and determining the volume and uncertainty for a rectangular box.
Explanation:The question asked concerns finding the center of mass of a triangular sandwich after taking a semicircular bite out of it, which is a problem related to geometry and mass distribution. When solving such problems, one would typically have to calculate the area of the original triangle and the area of the semicircular bite, then find the centroid of both shapes.
For the rectangular box's volume and uncertainty, this is a measurement and uncertainty calculation question. Here, one must apply the formula for the volume of a rectangle (length imes width imes height) and use the rules of propagation of uncertainty to calculate the overall uncertainty of the volume measurement.
The population of deer in a given park is modeled by y = d(x) = A( 1 2 )x + B, where x is the elapsed time in years since 2019. According to the model, which is the best prediction of the number of deer in the park in 2099?
A) A
B) B
C) A + B
D) A − B
Answer:
Step-by-step explanation:
The answer is B) B :)
Answer:
The answer is B
Step-by-step explanation:
According to USA Test prep it says so, but i didn't quite get the explanation so bear with me. Thank you :)(:
How many 1/5 liter glasses can Lin fill with a 1 1/2 liter bottle of water?
Answer:
The number of 1/5 liter glasses that Lin can fill is [tex]7\frac{1}{2}[/tex]
Step-by-step explanation:
we know that
To find out how many 1/5 liter glasses can Lin fill with a 1 1/2 liter bottle of water, divided 1 1/2 by 1/5
so
[tex]1\frac{1}{2} :\frac{1}{5}[/tex]
Convert mixed number to an improper fraction
[tex]1\frac{1}{2}=1+\frac{1}{2}=1\frac{1*2+1}{2}=\frac{3}{2}[/tex]
substitute
[tex]\frac{3}{2} :\frac{1}{5}[/tex]
Multiply in cross
[tex]\frac{5*3}{2*1}=\frac{15}{2}=7.5[/tex]
Convert to mixed number
[tex]7.5=7+\frac{1}{2}=7\frac{1}{2}[/tex]
Lin can fill 7.5 glasses of water from a 1 1/2 liter bottle. However, if only full glasses are counted, Lin can fill 7 full glasses.
Explanation:The question asks how many 1/5 liter glasses can be filled with a 1 1/2 liter bottle of water. To answer this, we need to perform a division of the total volume of the water by the volume of each glass.
First, express both quantities in the same units, in liters. The bottle has 1 1/2 liters, which is the same as 1.5 liters. Now, divide the total volume of the water by the volume of one glass:
1.5 liters / (1/5 liter per glass) = 1.5 * 5 = 7.5 glasses.
Therefore, Lin can fill 7.5 glasses of water from a 1 1/2 liter bottle, if we consider that partial glasses can be filled. If only full glasses can be filled, Lin can fill 7 full glasses.
A survey of 260 families show that 99 had dog 76 had cat 34 had dog and cat 98 had neither a cat nor a dog nor a parakeet 8 had a cat a dog and a parakeet
The number of parakeet is 21.
The calculation is as follows:
Let us assume the families had parakeet only be X
A survey of 260 families show that:
The families had a dog and a cat only it means
= 34 - 8
= 26
The families had a dog only is
= 99 - (26 + 8 )
= 65
The families had a cat only is
= 76 - (26 + 8)
= 42
So,
X = 260 - ( 98 + 8 + 26 + 65 + 42 )
= 260 - 239
= 21
Therefore, the families had a parakeet only is 21.
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The question pertains to the analysis of survey data relating to pet ownership among a set of families. It requires understanding of data analysis in mathematics.
Explanation:The question is about finding the total number of families that have each specified type of pet (dogs, cats, both dogs and cats, or a dog, a cat, and a parakeet). The given data from the survey states that among the 260 families:
99 had a dog 76 had a cat 34 had both a dog and a cat 98 had neither a dog nor a cat nor a parakeet 8 had a dog, a cat, and a parakeet
Using this data, you can compute and analyze the number of families owning each type of pet or combination of pets. It's important to understand that some families may fall into multiple categories - for example, families with a dog and a parakeet would count both towards the 'dog' total and the 'dog, cat, and parakeet' total.
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Which number line represents the solutions to |x – 5| = 1?
Answer:
x = 4, 6
Step-by-step explanation:
The line would go from 4 to 6 with closed circles at each point
(Add images of the lines provided if you need clarification)
Pirate Jack has an equal number of gold and silver coins. If Pirate Jack splits all of his coins into 7 equal piles for his parrots, he has 4 coins left. Or, if he splits all of his coins into 11 equal piles for his shipmates, he has 4 coins left. Assuming every pile has at least 1 coin, what is the least possible number of coins Pirate Jack has?
The least possible number of coins Pirate Jack has, is 81 coins.
Step-by-step explanation:
Given,
When the coins are divided into 7 equal piles, 4 coins are left.
When the coins are divided into 11 equal piles, 4 coins are left.
We will take LCM of both 7 and 11.
7 = 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, ....
11 = 11, 22, 33, 44, 55, 66, 77, 88, ...
The least common multiple of 7 and 11 is 77.
As 4 coins are left, therefore, we will add those coins.
Total possible coins = 77+4 = 81
The least possible number of coins Pirate Jack has, is 81 coins.
Keywords: LCM, addition
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!!! need help!! whats the answer?
a. The seats are divided into 40 different sections thats are given in only 5 sections, what
is the probability of a guest's sitting in a section that gets a hat?
The sum of two numbers is 14. Their difference is –146. Find the numbers.
Answer:
-66, 80
Step-by-step explanation:
Let x represent the first number. Then the second number is 14-x, and the difference is ...
x - (14-x) = -146
2x = -132 . . . . . . add 14, collect terms
x = -66 . . . . . . . . the first number
14-x = 14-(-66) = 80 . . . . . . the second number
Answer:
-66 & 80
Step-by-step explanation:
Let the two numbers be x and y
x + y = 14 (1)
x - y = -146 (2)
Adding (1) & (2),
2x = -132
x = -66
y = 14 - x = 14 - (-66) = 14 + 66
y = 80