Luisa is solving an equation on the bottom of a page. The corner of the page where the
equation is written is torn off as shown below.
7(x + 3) = 7(x + 5)
Luisa knows only one number was torn off, and she knows that the equation has an infinite number of solu-
tions. What must be the missing number?
A 2
B 14
C 21
D 35
To solve the equation 7(x + 3) = 7(x + 5), we can start by simplifying both sides of the equation:
7x + 21 = 7x + 35
Subtracting 7x from both sides, we get:
21 = 35
This is a contradiction, as 21 is not equal to 35. Therefore, the equation has no solution.
However, the problem states that the equation has an infinite number of solutions. This can only happen if the missing number is a factor that appears on both sides of the equation, and therefore cancels out when we simplify the equation.
Looking at the equation, we can see that both sides have a factor of 7, which cancels out when we simplify the equation. Therefore, the missing number must be the factor that was torn off, which is 7 multiplied by the difference between the two numbers inside the parentheses:
7(5 - 3) = 14
Therefore, the missing number is 14, which corresponds to answer option B.
FIRST ANSWER WILL GET 100 PTS!
What mixed number is equivalent to 21 ÷ 4?
Answer:
Step-by-step explanation:
5 1/4
Answer:là
5
với số dư
1
.
5
1
4
Step-by-step explanation:
del puerto de cabo San Lucas México salen dos barcos el barco México 1,navega con una trayectoria de x+y=88;el barco México 2 navega con una trayectoria de 2x + 2y= -176 en que punto se encontrarán los dos barcos?
how much is twice the size if im 3 ft 7 in tall
Answer:
the answer is 7.1 inches tall
Does anyone know how to do this Venn diagram question?
Answer:
\(\frac{8}{30}\)
Step-by-step explanation:
Card(AUBUC)= Card(A)+card(B)+card(C)-Card (A∩B) -Card( A∩C)-Card(B∩C) +Card(A∩B∩C)
= 21 + 14 + 15 - 10 - 8 - 4 + 2
= 30
Then
Card(AUBUC) = 30
Card( A∩C) = 2 + 6 = 8
\(p\left( A\cap C\right) =\frac{card\left( A\cap C \right) }{card\left( A\cup B\cup C \right) }\)
\(=\frac{8}{30}\)
pls help me with this math question pls
Answer:
Hey mate.....
Step-by-step explanation:
This is ur answer....
Triangle fixed value = 180= 180 - (112 + 47)
= 180 - 159
= 21
Hope it helps you,
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Suppose 5 quarts of a solution that is15% antifreeze is mixed with quarts 3 of a solution that is antifreeze 65% . Answer the questions below.
1. .35(15) + .72(5) = 8.85
2.8.85/(15 + 5) = 0.4425 = 44.25%Answer:
Step-by-step explanation:
P=x-2 ÷ x+1 for whar value of x is P equal to zero
Answer:
x = 2
Step-by-step explanation:
P = \(\frac{x-2}{x+1}\)
P will equal zero when the numerator is equal to zero , that is
x - 2 = 0 ( add 2 to both sides )
x = 2
P = 0 when x = 2
Name an acute angle and give its measure.
Angle: ______ Measure: _____
Name an obtuse angle and give its measure. (2 points)
Angle: _____ Measure: _____
Name one right angle. (1 point
Name one straight angle. (1 point)
11. Angle KEF = 40°, Angle KEJ = 50°
12. Angle HEF = 115°, Angle KED = 140°
13. Angle JEF = 90°, Angle KEF = 90°
14. Angle DEF = 180°
Define the term geometry?The study of points, lines, and shapes in two and three dimensions, as well as their properties and relationships, is the focus of the mathematical discipline known as geometry.
11. Acute angles: Those angles are less than 90 degree angles.
Angle KEF = 40°
Angle KEJ = 50°
Angle KEH = 75°
Angle JEH = 25°
Angle HED = 65°
12. Obtuse angles: Those angles are more than 90 degree angles.
Angle HEF = 115°
Angle KED = 140°
13. Right angle: Those angles are 90 degree angle.
Angle JEF = 90°
Angle KEF = 90°
14. Straight angle: Those angles make 180 degree angle.
Angle DEF = 180°
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please
\(2x {}^{2} + 2y {}^{2} - 6y - 12y = 3 \)
I need help
Can anyone help me with this?
Hey there! Welcome to Brainly! I'm happy to help you!
ANSWER A
If two events is mutually exclusive, it means that they cannot occur at the same time. Coin tossing is an example of something being mutually exclusive, landing on heads and tails cannot happen at the same time; it's either one or the other! In our case, this is not the case. The pizza having mushrooms on it does not affect the type of crust. The crust type and mushrooms can happen at the same time; you can have both! Therefore, Thick Crust Pizza and Pizza with mushrooms are not mutually exclusive.
ANSWER B
ANSWER 1: We know that there are nine pizzas in the oven. Looking at the chart, we see that three total pizzas have thick crust. One of them has no mushrooms and two of them do have mushrooms. This probability is 3/9, or 1/3.
ANSWER 2: We want to find a pizza that has both mushrooms and a thick crust. As we saw when solving for Answer 1, we have that 2 pizzas have both thick crust and mushrooms. This probability is 2/9.
ANSWER C
A dependent event is one that will depend on the result before it. Thick crust pizza and mushrooms do not affect each other at all; they do not depend on each other. They both do their own thing. We need to justify with things we found in Answer B. Well, when we added the event of mushrooms our probability decreased. If one of the events depended on the other, the probability would have definitely increased. Therefore, these events are both independent.
I hope that this helps you! Have a wonderful day!
An investigator claims, with 95 percent confidence, that the interval between 10 and 16 miles includes the mean commute distance for all California commuters. To have 95 percent confidence signifies that
Answer:
Hello the options to your question is missing below are the options
A) if sample means were obtained for a long series of samples, approximately 95 percent of all sample means would be between 10 and 16 miles
B.the unknown population mean is definitely between 10 and 16 miles
C.if these intervals were constructed for a long series of samples, approximately 95 percent would include the unknown mean commute distance for all Californians
D.the unknown population mean is between 10 and 16 miles with probability .95
Answer : if these intervals were constructed for a long series of samples, approximately 95 percent would include the unknown mean commute distance for all Californians ( c )
Step-by-step explanation:
95% confidence
interval = 10 to 16 miles
To have 95% confidence signifies that if these intervals were constructed for a long series of samples, approximately 95 percent would include the unknown mean commute distance for all Californians
confidence interval covers a range of samples/values in the interval and the higher the % of the confidence interval the more precise the interval is,
explain why the statement x < 3 or > 5 cannot be written 5 < x < 3
Answer:
This formula has no values, it is a false inequality. X can not be greater than 5, and less than 3.
Step-by-step explanation:
x < 3 or x > 5
This means, x is less than 3, but greater than 5.
Technically, you would write this as 5 < x < 3, however, this is a false inequality, and does not work.
express 35 as a fraction of 70,give answer in its simplest form
Find the following angle measures.
mL EAD
mL CAB
The measure of ∠EAD = 29° and ∠CAB = 119°.
How many pairs of vertically opposite pairs are formed when 2 lines intersect?When two lines intersect, 2 pairs of vertically opposite angles are formed.
Given is the figure as attached with the question.
The measure of ∠EAD = 90 - 61 = 29°
∠EAD = 29°
∠CAB = ∠EAF = 90° + 29° = 119° {vertically opposite angles are equal}
∠CAB = 119°
Therefore, the measurement of ∠EAD = 29° and ∠CAB = 119°.
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The side of a triangle are in the ratio 4:4:3 what kind of triangle is it (b) calculate the smallest angle of the triangle to the nearest degree
The smallest angle of the equilateral triangle is 60 degrees
If the sides of a triangle are in the ratio 4:4:3, it implies that the lengths of the sides are proportional.
To determine the type of triangle, we examine the side lengths. Since all three sides are equal in length, we have an equilateral triangle.
For an equilateral triangle, all angles are equal. To calculate the smallest angle, we divide the total sum of angles in a triangle (180 degrees) by the number of angles, which is 3:
Smallest angle \(= \frac{180}{3} = 60\)\) degrees.
Therefore, the smallest angle of the equilateral triangle is 60 degrees (to the nearest degree).
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The common factors of 36, 240, and 504
Answer: 1, 2, 3, 4,6 12
Step-by-step explanation:
every single number can be divided by the answer numbes
1.Two-fifth of the sum of a number and 24 is equal to 5 times the number decreased by 18, find the number.
2. sketch the parabola y=x^2 + 4x + 96, show all intercept, the axis symmetry and vertex
The solution is
a) The number is 6
b) The equation of the parabola is y = x² + 4x + 96 with vertex ( -2 , 92 ) and the y intercept is ( 0 , 96 ) and the axis of symmetry is x = -2
What is a Parabola?
A Parabola, open curve, a conic section produced by the intersection of a right circular cone and a plane parallel to an element of the cone. A parabola is a plane curve generated by a point moving so that its distance from a fixed point is equal to its distance from a fixed line
The equation of the parabola is given by
( x - h )² = 4p ( y - k )
where ( h , k ) is the vertex and ( h , k + p ) is the focus
y is the directrix and y = k – p
The equation of the parabola is also given by the equation
y = ax² + bx + c
where a , b , and c are the three coefficients and the parabola is uniquely identified
Given data ,
a)
Let the equation be represented as A
Now , the value of A is
Let the number be = n
A = Two-fifth of the sum of a number and 24 is equal to 5 times the number decreased by 18
Substituting the values in the equation , we get
2/5 ( n + 24 ) = 5n - 18
On simplifying the equation , we get
Multiply by 5 on both sides of the equation , we get
2 ( n + 24 ) = 25n - 90
2n + 48 = 25n - 90
Subtracting 2n on both sides of the equation , we get
23n - 90 = 48
Adding 90 on both sides of the equation , we get
23n = 138
Divide by 23 on both sides of the equation , we get
n = 6
Therefore , the number is 6
b)
The equation of parabola is given as
y = x² + 4x + 96
Now , the equation can be simplified as
y = (x + 2)² + 92
The equation of the parabola is given by
( x - h )² = 4p ( y - k )
where ( h , k ) is the vertex and ( h , k + p ) is the focus
Substituting the values in the equation , we get
The vertex of the parabola is P ( -2 , 92 )
The y intercept of the parabola is ( 0 , 96 )
The axis of symmetry of parabola is x = -2
Hence , the equation of parabola is y = (x + 2)² + 92
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what’s the missing side length help please
Answer:
6.5
Step-by-step explanation:
\(a^{2} + b^{2} = c^{2}\) means that the two shorter legs (a and b) squared and added together equal the hypotenuse (c) you square \(6^{2} + 2.5^{2} = 42.25\) then find the square root of 42.25 which is 6.5
fill in the mission numbers to make the fractions equivalent. 1/2 and /8= 4/12 and /60= 2/3 and /12= 4/4 and /8=
To make the fractions equivalent, we need to find the missing numerators that would make them equal. Let's fill in the missing numerators:
1/2 and __/8
To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 4:
1/2 and 4/8
Now, the fractions are equivalent.
---
4/12 and __/60
To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 5:
4/12 and 20/60
Now, the fractions are equivalent.
---
2/3 and __/12
To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 4:
2/3 and 8/12
Now, the fractions are equivalent.
---
4/4 and __/8
To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 2:
4/4 and 8/8
Now, the fractions are equivalent.
Which graph represents the function f(x)=4x?
Responses
Answer:
slope = 4
points on graph = (0,0), (1,4)
Step-by-step explanation:
line going through quadrants 1 and 3. Straight line.
Find the equation of the linear function represented by the table below in slope-
intercept form.
Answer:
y=2x+6
Step-by-step explanation:
Neil pays 2.16 in postage to a frien he uses 40 cent stamps and 7cent stamps to 2.16 how many of each stamps did he use
Find the area of the region bounded by the equations by integrating (i) with respect to x and (ii) with respect to y. x=16-y^2 x=y-4
The area of the region bounded by the equations by integrating with respect to x and with respect to y is 352.
To find the area of the region bounded by the equations x = 16 - y^2 and x = y - 4, we can integrate with respect to either x or y. To do it with respect to x, we set up the integral: Area = ∫[lower curve]^[upper curve] (upper curve - lower curve) dx = ∫4^12 (x + 4 - sqrt(16 - x)) dx, where the lower curve is y = sqrt(16 - x) and the upper curve is y = x + 4. We then evaluate this integral by splitting it into two parts and evaluating each part separately: ∫4^8 (x + 4 - sqrt(16 - x)) dx + ∫8^12 (x + 4 - sqrt(16 - x)) dx = 112 + C + 240 + C = 352 + 2C = 352. Thus, the area of the region is 352.
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Which equation is equivalent to 2 Superscript 4 x Baseline = 8 Superscript x minus 3?
2 Superscript 4 x Baseline = 2 Superscript 2 x minus 3
2 Superscript 4 x Baseline = 2 Superscript 2 x minus 6
2 Superscript 4 x Baseline = 2 Superscript 3 x minus 3
The equivalent exponential equations are given as follows:
\(2^{4x} = 2^{3(x - 3)}\)
How to obtain the equivalent exponential expression?The exponential expression for this problem is defined as follows:
\(2^{4x} = 8^{x - 3}\)
The number eight is the third power of 3, that is:
8 = 2³.
The power of a power rule is used when a single base is elevated to multiple exponents.
Then the simplified expression is obtained keeping the base, while the exponents are multiplied.
Meaning that the equivalent expression on the right side of the equality in this problem is given as follows:
\(8^{x - 3} = (2^3)^{x - 3} = 2^{3(x - 3)}\)
Meaning that the correct option is given by the fourth option.
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If sin x=0.2, write down the values for sin (pi-x)
If the value of sin x = 0.2, then the values for sin(π - x) is 0.2.
Given that,
the value of sin x = 0.2
We have to find the value of sin(π - x).
We know the trigonometric rule that,
sin(π - x) = sin (x)
for any value of x.
So here whatever the value of x, the value of sin(π - x) is sin (x) itself.
So here sin x = 0.2.
So, by the rule,
sin(π - x) = sin (x) = 0.2
Hence the value is 0.2.
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How do I do this problem?
Answer:
hey you can use scan and search
Answer:
I got : 0.42264973
Step-by-step explanation:
1/ -√3 + 1
-√3 = -1.73 ( 2 decimal place )
1/ -1.73 + 1
and found the answer
how would i anwser this? help pls!
Answer:
Step-by-step explanation:
To get the y values all you need to do is substitute the x value in the equation y=-2/3x+7.
For example:
y=-2/3(-6)=7
-2/3x6=-4
-4+7=3
(-6,3)
You can double check your work by filling the x and y coordinates in the equation and when solved if it it true you know you were correct.
To get the x value, you need to fill in the y in the equation y=-2/3x+7
for example:
5=-2/3x+7
-2=-2/3x
3=x
(3,5)
y=-2/3x+7
y=-2/3(15)+7
y=-10+7
y=-3
(15,-3)
y=-2/3x+7
15=-2/3x+7
8=-2/3x
-12=x
(-12,15)
Convert .805 liters to millimeter s
This simple question does not require any statistical calculations, only statistical knowledge. The showerhead heights at a men’s athletic locker room were designed to be 72 inches which is well above the mean height of 69.5”. The heights of the athletes are normally distributed. From the choices listed below, which is more likely to be true: a, b or c?
a.The mean height for a randomly selected sample of 20 players is more than 72 inches.
b.The height of one randomly selected player is more than 72 inches.
c.Both a and b are equally likely.
Why? (Justify your answer with a short answer.)
That both a and b are equally likely, is also not true since the Probability of option b is higher than that of option a.
Option b is more likely to be true. This is because the given information states that the showerhead heights were designed to be 72 inches, which is well above the mean height of 69.5 inches. Therefore, it is reasonable to assume that the majority of the players' heights are below 72 inches. Since the heights of the athletes are normally distributed, the probability of selecting a player at random with a height above 72 inches is relatively low. On the other hand, option a suggests that the mean height of a sample of 20 players is more than 72 inches, which is less likely than option b. Option c, which suggests that both a and b are equally likely, is also not true since the probability of option b is higher than that of option a.
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