Answer:2 in.
Step-by-step explanation:
Given
Dimension of photo frame is [tex]20\ in.\times 24\ in.[/tex]
If the photo cover an area of [tex]320\ in.^2[/tex]
Suppose x be the width of border
Therefore dimension of frame without border is
[tex]A'=(20-2x)(24-2x)[/tex]
And [tex]A'[/tex] must be equal to [tex]320\ in.^2[/tex]
So,
[tex]\Rightarrow (20-2x)(24-2x)=320[/tex]
[tex]\Rightarrow (10-x)(12-x)=80[/tex]
[tex]\Rightarrow 120-10x-12x+x^2=80[/tex]
[tex]\Rightarrow x^2-22x+40=0[/tex]
[tex]\Rightarrow x^2-20x-2x+40=0[/tex]
[tex]\Rightarrow (x-2)(x-20)=0[/tex]
Thus there are two values of x out of which [tex]x=20\ in.[/tex] is not valid because it is not feasible
thus width of border is [tex]x=2\ in.[/tex]
What are the solutions of the quadratic equation 49x2 = 9?
Answer:
49x^2 - 9 = 0
As there is no x term, we can pretty much guess we have a situation where we factlrise by something known aa difference of two squares, so to factorise it:
49 = 7^2
9 = 3^2
x^2 = (x)^2
so...
(7x - 3)(7x + 3) = 0
7x - 3 = 0 7x + 3 = 0
x = 3/7 x = -3/7
Step-by-step explanation:
ANSWER ASAP!
How many solutions does this system have?
y=3x-5
y=-x+4
one
two
an infinite number
no solution
2 Points
Classify the following triangle. Check all that apply.
Which congruence theorem can be used to prove △ABC ≅ △DEF?
Answer:
Hope this helps! If it doesn't let me know and I will try and answer it better!
Step-by-step explanation:
HL Congruence Theorem
This shows that _ AC ≅ . Therefore, △ABC ≅ △DEF by . Use the HL Congruence Theorem to prove that the triangles are congruent. A Given: ∠P and ∠R are right angles.
Find the surface area of a cylinder with a base radius of 4m and a height of 5m.
Write your answer in terms of pi, and be sure to include the correct unit.
Answer:
A≈226.19
Step-by-step explanation:
The formula is A=2πrh+2πr²
you fill in the radius and get A=2π4h+2π4²
Then fill in the height and get A=2π4×5+2π4²
and your final answer would be A≈226.19
What is the slope between the points (0,–5) and (–9,1)?
The slope between the points (0, –5) and (–9,1) is -2/3, which is found using the slope formula. Positive slopes rise, negative slopes fall, and zero slopes are horizontal lines.
Explanation:To find the slope of a line passing through two points (0, –5) and (–9,1), we use the formula for the slope (m), which is m = (y₂ - y₁) / (x₂ - x₁), where (x₁, y₁) and (x₂, y₂) are the coordinates of the two points.
Substituting the given points into the formula, we get m = (1 - (-5)) / (-9 - 0), which simplifies to m = (1 + 5) / (-9), and further simplifies to m = 6 / (-9), resulting in a slope of m = -2/3.
Regarding slope and its characteristics on a graph, a positive slope means the line rises as it moves from left to right, a negative slope means the line falls as it moves from left to right, and a zero slope indicates a horizontal line.
The given number line shows the solutions to which inequality?
A)
x + 7 ≤ 5
B)
x + 3 ≥ 1
C)
x − 5 > 2
D)
x − 1 ≤ 1
Answer:
A)
x + 7 < 5
Shows inequality
The correct inequality that represents the solutions on the given number line is C) [tex]\( x - 5 > 2 \).[/tex]
To find the correct inequality, we need to determine which one corresponds to the shaded portion of the number line. The shaded portion indicates the set of all [tex]\( x \)[/tex] values that satisfy the inequality.
Let's analyze each option:
A) [tex]\( x + 7 \leq 5 \)[/tex]
If we solve this inequality, we get:
[tex]\( x \leq 5 - 7 \)[/tex]
[tex]\( x \leq -2 \)[/tex]
This inequality would be represented by a number line shaded to the left of -2, including -2 itself. This does not match the given number line, which is shaded to the right of a point.
B) [tex]\( x + 3 \geq 1 \)[/tex]
Solving this inequality, we get:
[tex]\( x \geq 1 - 3 \)[/tex]
[tex]\( x \geq -2 \)[/tex]
This inequality would be represented by a number line shaded to the right of -2, including -2 itself. However, the inequality sign in the question is non-inclusive, which means -2 itself should not be shaded. This does not match the given number line, which has a shaded circle at the starting point of the shaded region, indicating inclusivity.
C) [tex]\( x - 5 > 2 \)[/tex]
Solving this inequality, we get:
[tex]\( x > 2 + 5 \)[/tex]
[tex]\( x > 7 \)[/tex]
This inequality would be represented by a number line shaded to the right of 7, not including 7 itself. This matches the given number line, which shows the shaded region starting just to the right of 7 (indicated by an open circle at 7).
D) [tex]\( x - 1 \leq 1 \)[/tex]
Solving this inequality, we get:
[tex]\( x \leq 1 + 1 \)[/tex]
[tex]\( x \leq 2 \)[/tex]
This inequality would be represented by a number line shaded to the left of 2, including 2 itself. This does not match the given number line, which is shaded to the right of a point and has an open circle at the starting point of the shaded region.
Therefore, the correct answer is C)[tex]\( x - 5 > 2 \)[/tex], as it accurately describes the shaded region on the given number line.
Suppose a normal distribution has a mean of 26 and a standard deviation of 4. What is the probability that a data value is between 27 and 28? Round your answer to the nearest tenth of a percent.
A. 12.3%
B. 9.3%
C. 10.3%
D. 11.3%
Answer:
Answer is B. 9.3
Step-by-step explanation:
I took the test
There is a probability of 9.3% that the normal distribution data value is between 27 and 28
What is z score?The z score is used to determine by how many standard deviations the raw score is above or below the mean. It is given by:
z = (raw score - mean)/standard deviation
Given that:
mean of 26 and a standard deviation of 4, For:
For x = 27:
z = (27 - 26) / 4 = 0.25
For x = 28:
z = (28 - 26) / 4 = 0.5
P(0.25 < z < 0.5) = P(z < 0.5) - P(z < 0.25) = 0.6915 - 0.5987 = 0.093
There is a probability of 9.3% that the normal distribution data value is between 27 and 28
Find out more on z score at: https://brainly.com/question/25638875
How do I find this?Please help!!!
Answer:
d) [tex]y=-\frac{1}{2} (x-3)^{2} -4[/tex]
Step-by-step explanation:
When you reflect an equation the slope is the opposite (if the slope is positive it'll be negative when reflected)
The slope is [tex]\frac{1}{2}[/tex] and when it is reflected it is [tex]-\frac{1}{2}[/tex]
When you shift something to the right you add [tex](x-3)^{2}[/tex]
I need help please and thank you
Answer:
28.26
Step-by-step explanation:
This is the formula for area of a circle
A = pi r^2
Substitute the given values
A = 3.14 (3)^2
A = 3.14 (9)
28.26
Can someone help me with this
Answer:
8/3 or 2 2/3 as a mixed number
Step-by-step explanation:
When you get ready to get dressed for school you open your closet to find that you have the following choices: a red, blue, or white shirt: jeans or sweatpants; tennis shoes or sandals how many different outfits could be made with these choices
Answer:Why would I know?
Step-by-step explanation: get good fam
Answer:
12
Step-by-step explanation:
So you know you need three different articles of clothing
There are three different types of shirts, two types of pants, and two types of shoes
All you do is simply multiple the three by two and then two again
If it helps to branch it out so you visually see it, that is a great option
but in sum, 3x2x2 is 12, so there are 12 different combos
PLS HURRY ILL GIVE BRAINLIEST
Which graph of ordered pairs shows a proportional relationship?
Answer:
B.)
Step-by-step explanation:
the pictures aren't loading but i think we have the same problem if this is on edge, b is a straight line that passes through the origin, a c and d do not line up
The graph of ordered pairs that shows a proportional relationship is: Graph 1
How to Identify the proportional relationship?A proportional relationship is defined as a relationship between two variables where the ratio of the variables is always the same. In other words, one variable is always a constant multiple of the other variable.
Graph 1: The rate of change of y with x for the two points are:
m = -2/1 = -2
m = -4/2 = -2
Graph 2: The rate of change of y with x for the two points are:
m = 3/1 = 3
m = -2/-2 = 1
Graph 3: The rate of change of y with x for the two points are:
m = -2/1 = -2
m = 1/-3 = --1/3
Graph 4: The rate of change of y with x for the two points are:
m = 1/2
m = 3/5
Thus, the only one that represents a proportional relationship is Graph 1
Read more about proportional relationship at: https://brainly.com/question/12242745
#SPJ3
I need help please :)
Help out please thank you
Answer:
x = 26
Step-by-step explanation:
The three angles form a straight line, so they will sum to 180
4x - 8 + 34 + 76- x = 180
Combine like terms
3x+ 102 = 180
Subtract 102 from each side
3x+102-102 = 180-102
3x= 78
Divide each side by 3
3x/3 = 78/3
x = 26
HELP A 13 YEAR OLD PLEASEEEEEEEEEEEEEEEEEE
Answer:
A and B
Step-by-step explanation:
also hey becky!
WZ = 5.3 km, find the area of the shaded sectors to the nearest tenth. Please help
Answer: The area of the shaded sectors is 35.3 square kilometres
Step-by-step explanation: What we have here is a circle with center Z. Two sectors have been formed which are ZVW and ZYX. A careful observation reveals that both sectors are similar. If WY passes through the center Z then WY is a diameter. The same applies to VX, since it also passes through the center, therefore it is a diameter. Both lines intersect at the center, that makes both sectors to have the same radii which is 5.3 km and same applies to the angle subtended at the center of the sector, both angles are opposite angles formed by intersecting lines (opposite angles formed by intersecting lines are equal). On a straight line WY, the sum of angles ∠WZX and ∠YZX equals 180 degrees (Sum of angles on a straight line equals 180). Therefore;
WZX + YZX = 180
108 + YZX = 180
Subtract 180 from both sides of the equation
YZX = 72°
Therefore the area of shaded sector YZX is given as;
Area of a sector = (∅/360) x πr²
Where ∅ is 72, and r is 5.3
Area of sector = (72/360) x 3.14 x 5.3²
Area of sector = 0.2 x 3.14 x 28.09
Area of sector = 17.64
Having in mind that both sectors are similar (the same radii and the same central angle), the area of the shaded sectors shall be equal to 17.64 times 2 and that equals 35.28. (That is approximately 35.3 to the nearest tenth)
The area of the shaded sectors therefore is 35.3 square kilometres (35.3 km²)
Answer:
Area of the shaded region ≈ 35.3 km²
Step-by-step explanation:
Area of a sector = ∅/360 × πr²
angle on a straight line = 180°
Therefore,
∠vzw = 180 - 108 = 72°
∠yzx = 180 - 108 = 72°
Area = 72 /360 × 22/7 × 5.3²
Area = 72 /360 × 22/7 × 28.09
Area = 44494.56/2520
Area = 17.656571429
Area = 17.66 km²
The area is one portion of the shaded part , the area of the 2 shaded sector will be
Area of zvw + Area of zyx
Both area are same . They have same radius and the same angle.
Area of the shaded region = 17.66 + 17.66
Area of the shaded region ≈ 35.3 km²
Please Help. Find the value of x in the isosceles triangle shown below
Answer:
the answer is 6
Step-by-step explanation:
By pytagoras Theorem
hope its helpful
Please help !! :) 30 points.
Which could be measured in meters?
A. the weight of a whale
B. the amount of juice to buy
c. the length of a soccer field
D. the time it takes to run a mile
E. the temperature in summer
Answer:the length of a soccer field
PLZ GIVE ME BRAINLIEST
C.
Step-by-step explanation:
Deena and Jackson tossed two coins at the same time. In five tosses, Deena got heads on both coins three times. In
50 tosses, Jackson got heads on both coins 12 times. What does this illustrate about theoretical and experimental
probability that both tossed coins will be heads?
A- Experimental probability is not affected by sample size
B- Experimental probability approaches theoretical probability when the sample size is large.
C- Smaller groups give more accurate results.
D- Larger groups have greater chance for error
What is the scale factor of figure A to figure B?
What is the length of jL
Answer:
The length of JL is 18 feet
Step-by-step explanation:
This is true because the sides double in length
Answer:
18 ft
Step-by-step explanation:
The triangles are similar so the ratios must be the same
GI IH
--------- = -------------
JL LK
9 12
--------- = -------------
JL 24
Using cross products
9 *24 = JL *12
Divide each side by 12
9*24/12 = JL*12/12
18 = JL
Find the Slope
Screenshot attached
Answer:
red one
Step-by-step explanation:
you do rise over run
Answer:
4/3
Step-by-step explanation:
you are going up 4 and right 3 therefore its positive because if it were negative it would be down 4 left 3
What does this equal?
Answer:
x²y²+xy²+3+xy+2y²
Step-by-step explanation:
(2x²y²+x²y+xy²+3)-(x²y²+x²y²+x²y-xy-2y²)
1. remove the parentheses (when there’s - in front of an expression in parentheses change the sign of each term of the expression)
2x²y² + x²y + xy² + 3-x²y² - x²y² - x²y + xy - 2y²
2. eliminate the opposites
2x²y² + xy² + 3 -x²y² + xy +2y²
3. collect like terms
x²y² + xy² + 3 + xy + 2y²
find the exact length of the third side
Answer:
9
Step-by-step explanation:
a triangle is bacicly half of a rectangle so 3 x 6 is 18 but since it's just half, you divide by 2 and you get 9!
Step-by-step explanation:
Phytagoras Theorem :
c² = a² + b²
c² = 3² + 6²
c² = 9 + 36
c² = 45
c = √45
So, the exact length og the third side is √45
Hope it helpful and useful :)
What is the 6th term in this geometric sequence? 5, -15, 45, -135
Answer:
-1215.
Step-by-step explanation:
For a geometric sequence:
nth term = a1 r^(n-1)
The first term a1 = 5 and the common ratio r = -15/5 = -3.
So 6th term = 5 * (-3)^(6-1)
= 5 * (-3)^5
= -1215.
The 6th term in this geometric sequence should be considered as the -1215.
Calculation of the 6th term:The following formula should be used for the same.
nth term = [tex]a_1\ r^{(n-1)[/tex]
Here,
The first term a1 = 5
and the common ratio r = [tex]-15/5[/tex]= -3.
So 6th term should be
[tex]= 5 \times (-3)^{(6-1)}[/tex]
[tex]= 5 \times (-3)^5[/tex]
= -1215
Hence, The 6th term in this geometric sequence should be considered as the -1215.
Learn more about geometric here: https://brainly.com/question/16009711
$2.95 for a notebook plus 7% tax.
I need help with this
Can you include steps please
Answer:
$3.16
Step-by-step explanation:
$2.95 + 7%= 3.1565
by rounding up you get $3.16.
Answer:
$3.16
Step-by-step explanation:
To find the total, find how much the tax is. Multiply the price of the notebook by the percentage the tax is.
$2.95 × 0.07 = $0.21
Add the value of tax with the price of the book.
$2.95 + $0.21 = $3.16
You can also solve this problem by multiplying the price of the notebook by the percentage of the tax plus one.
$2.95 × 1.07 = $3.16
At the beginning of summer, the water level on a pond is 2 feet below its normal level. After an unusually dry summer, the water level on the pond dropped another 2 feet. How far above or below the normal water level is the pond at the end of the summer?
Answer:
Step-by-step explanation:
Tell whether the line or segment is best described as a radius, chord, diameter, secant, or tangent of ⨀O
.
Answer:
Can you please provide a picture of the line/segment?
Step-by-step explanation:
Radius: line from center of circle to side
Diameter: double the radius, goes straight through middle of circle
Secant: line that intersects the circle in two different points
Chord: line that intersects the circle in exactly one point, called the point of tangency
hope that helps :)
Help with my homework!
Answer:
a) 72 cm2 (centimeter square)
b) 9 cm2 (centimeter square)
c) 9 cm2 (centimeter square)
d) 54 cm2 (centimeter square)
Step-by-step explanation:
a) the area of the rectangle = Base x Height
= 12 x 6
= 72 cm2 (centimeter square)
b) the area of the triangle A = 1/2 x Base x Height
= 1/2 x 3 x 6
= 9 cm2 (centimeter square)
c) the area of the triangle B = 1/2 x Base x Height
= 1/2 x 3 x 6
= 9 cm2 (centimeter square)
d) area of the parallelogram = area of the rectangle - area of triangle A - Area of triangle B
= 72 - 9 - 9
= 54 cm2 (centimeter square)