99 boys and 1 girl makes 99 percent of boys. To make it 98%, 50 boys must leave the theatre, so there are 49 boys and 1 girl, making 98% of boys.
Solve for x : 2|x-1|+5<13
Hi there!
2|x - 1| + 5 < 13
Begin by subtracting 5 from both sides:
2|x - 1| < 8
Divide both sides by 2:
|x - 1| < 4
Find both the positive and negative solutions:
x - 1 < 4
x < 5
-(x - 1) < 4
-x + 1 < 4
-x < 3
x > -3
[tex]Hello[/tex] [tex]There![/tex]
Let's solve your inequality step-by-step.
[tex]2(|x-1|)+5<13[/tex]
Step 1:
You must add -5 both sides.
[tex]2(|x-1|)+5+-5<13+-5[/tex]
[tex]2(|x-1|)<8[/tex]
Step 2:
You must divide both sides by 2.
[tex]\frac{2(|x-1|)}{2}[/tex] [tex] \leq \frac{8}{2}[/tex]
[tex]|x-1|<4[/tex]
Step 3:
Solve the Absolute Value.
[tex]|x-1|<4[/tex]
We know that x−1<4 and x−1>−4.
[tex]x-1<4[/tex] Condition 1.
[tex]x-1+1<4+1[/tex] (Add 1 to both sides)
[tex]x<5[/tex]
[tex]x-1>-4[/tex] (Condition 2)
[tex]x-1+1>-4+1[/tex] (Add 1 to both sides)
[tex]x>-3[/tex]
[tex]ANSWER![/tex]
[tex]x<5[/tex] [tex]and[/tex] [tex]x>-3[/tex]
Hopefully, this helps you!!
[tex]AnimeVines[/tex]
Plz Help...............I’ll give you 50 pts
1. Essential Question How do you use what you know about absolute value to add integers?
2. Reasoning How can you tell the sign of the sum of a positive and negative integer without doing any calculations?
3. Model with Math How would you use a number line to determine the sum of two negative integers?
Do You Know How?
4. Sarah bought a bike that cost $260. She had a coupon that was worth $55 off the cost of any bike. Use the expression 260 + (-55) to find how much Sarah paid for her bike.
5. A shark is swimming 60 feet below the surface of the ocean. There is a fish that is 25 feet deeper in the water. Use the expression (-60) + (-25) to describe the fish’s location relative to the surface of the ocean.
60 feet
25 feet
6. The high temperature one day was 30°F. Then the temperature dropped 23 degrees during the night. Does the expression 30 + (-23) represent the temperature at night? Explain.
Answer:
1) I know that if the two integers have the same sign: Add their absolute values and give the answer the same sign as the two original integers. Also, I know that If the two integers have different signs: Subtract the lesser absolute value from the greater absolute value.
2) To find the sum of a positive and a negative integer, take the absolute value of each integer and then subtract these values. The result takes the sign of the integer with the larger absolute value. The sum of any integer and its opposite is equal to zero.
3) First, draw a number line. Then, find the location of the first integer on the number line. Next, if the second integer is positive, move that many units to the right from the location of the first integer. If the second integer is negative, move that many units to the left from the location of the first integer.
4) 205 dollars
5) The fish’s location relative to the surface of the ocean is -85
6) Honestly, I'm not so sure about this now, but I believe yes.
Step-by-step explanation:
there are a lot of resources, here on this app, that i used to help answer your question. If I helped, it would be nice if you rated this brainliest, give 5 stars, and the 50 points :)
1) I know that if the two integers have the same sign: Add their absolute values and give the answer the same sign as the two original integers. Also, I know that If the two integers have different signs: Subtract the lesser absolute value from the greater absolute value.
2) To find the sum of a positive and a negative integer, take the absolute value of each integer and then subtract these values. The result takes the sign of the integer with the larger absolute value. The sum of any integer and its opposite is equal to zero.
3) First, draw a number line. Then, find the location of the first integer on the number line. Next, if the second integer is positive, move that many units to the right from the location of the first integer. If the second integer is negative, move that many units to the left from the location of the first integer.
4) $205
5) The fish’s location relative to the surface of the ocean is -85 or -25 if the fish is 25 feet deeper from surface of ocean
6) Yes if both the temperatures are in Degree Fahrenheit
please click thanks and mark brainliest if you like :)
The velocity of a bus increases from 72km/hr to 30m/s in 10 seconds. Calculate its acceleration
Answer:
I think this will help you
(x-3).(x+3)-(x+5).(x-1)
Need help! Please answer quickly! :)
Answer: a
Step-by-step explanation:
Find the measure of each angle indicated.
A) 95°
C) 26°
B) 92°
D) 20°
Answer:
D) 20°
Step-by-step explanation:
Using the triangle sum theorem, you know that every triangle's interior angles add up to 180°. Therefore the bottom triangle's missing angle can be found by giving it the variable x.
57° + 30° + x = 180°
Simplify: 87° + x =180°
x=93°
By the vertical angles theorem, the vertical angle directly across this angle is congruent to this one. Meaning that the top triangle's angle are 67°, 93°, and unknown, which we can assign y. We can use the same method from above here.
67° + 93° + y = 180°
Simplify: 160° + y = 180°
y=20°
Answer:
(C). 26°
Step-by-step explanation:
Answer all
1) 4x*3x
2) 2/3+ 1/4
[tex]\large\textsf{Hey there!}[/tex]
[tex]\large\textsf{\# 1.}[/tex]
[tex]\large\textsf{4x} \times\large\textsf{3x}[/tex]
[tex]\large\text{COMBINE the LIKE TERMS}[/tex]
[tex]\large\textsf{4x}\times\large\textsf{3x = \bf 12x}\mathsf{\bf ^2}[/tex]
[tex]\boxed{\boxed{\large\textsf{Answer: \bf 12x}\bf ^2}}\huge\checkmark[/tex]
[tex]\large\text{\# 2.}[/tex]
[tex]\mathsf{\dfrac{2}{3}+\dfrac{1}{4}}[/tex]
[tex]\mathsf{= \dfrac{2\times4+1\times3}{3\times4}}[/tex]
[tex]\mathsf{2 \times 4 = \bf 8}[/tex]
[tex]\mathsf{1 \times 3 = \bf 3}[/tex]
[tex]\mathsf{3\times 4 = \bf 12}[/tex]
[tex]\mathsf{= \dfrac{8 + 3}{12}}[/tex]
[tex]\mathsf{8 + 3 = \bf 11}[/tex]
[tex]\mathsf{= \dfrac{11}{12}}[/tex]
[tex]\boxed{\boxed{\large\textsf{Answer: }\mathsf{\bf \dfrac{11}{12}}}}\huge\checkmark[/tex]
[tex]\large\textsf{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Help please! will give brainiest
Answer:
cd a gimem ?
Step-by-step explanation:
In figure above, if l1 | | l2 then value of x is:
a) 40°
b) 50°
c) 80°
d) 100°
Answer:
its letter c so 80
Step-by-step explanation:
I hope this help
Given a triangle MTN, prove that
<m+<t+<n= 180° strictly
use m, T and N with other
Letters in your triangle.
Answer:
[tex]\angle m + \angle t + \angle n = 180[/tex]
Step-by-step explanation:
Required
Show that:
[tex]\angle m + \angle t + \angle n = 180^o[/tex]
To make the proof easier, I've added a screenshot of the triangle.
We make use of alternate angles to complete the proof.
In the attached triangle, the two angles beside [tex]\angle m[/tex] are alternate to [tex]\angle t[/tex] and [tex]\angle n[/tex]
i.e.
[tex]\angle 1 = \angle t[/tex]
[tex]\angle 2 = \angle n[/tex]
Using angle on a straight line theorem, we have:
[tex]\angle 1 + \angle m + \angle 2 = 180[/tex]
Substitute values for (1) and (2)
[tex]\angle t + \angle m + \angle n = 180[/tex]
Rewrite as:
[tex]\angle m + \angle t + \angle n = 180[/tex] -- proved
given that tan x =3/7find cos (90-x) giving you answer in 4 significant figures
Answer:
[tex]\cos \left(90 ^\circ - x\right) \approx 0.1688[/tex]
Step-by-step explanation:
We are given that:
[tex]\displaystyle \tan x = \frac{3}{7}[/tex]
And we want to find the value of:
[tex]\displaystyle \cos \left(90^\circ - x\right)[/tex]
Recall that by definition, tan(θ) = sin(θ) / cos(θ). Hence:
[tex]\displaystyle \frac{\sin x }{\cos x} = \frac{3}{7}[/tex]
And by definition, sin(θ) = cos(90° - θ). Hence:
[tex]\displaystyle \frac{\cos \left(90^\circ - x\right)}{\cos x} = \frac{3}{7}[/tex]
Multiply:
[tex]\displaystyle \cos \left(90 ^\circ - x\right) = \frac{3}{7} \cos x[/tex]
Find cosine. Recall that tangent is the ratio of the opposite side to the adjacent side. Therefore, the opposite side is 3 and the adjacent side is 7.
Thus, by the Pythagorean Theorem, the hypotenuse will be:
[tex]\displaystyle h = \sqrt{3^2 + 7^2} = \sqrt{58}[/tex]
Cosine is the ratio of the adjacent side to the hypotenuse. Therefore:
[tex]\displaystyle \cos x = \frac{7}{\sqrt{58}}[/tex]
Thus:
[tex]\displaystyle \cos \left(90 ^\circ - x\right) = \frac{3}{7} \left(\frac{3}{\sqrt{58}}\right)[/tex]
Use a calculator. Hence:
[tex]\cos \left(90 ^\circ - x\right) \approx 0.1688[/tex]
Explain the differences between adding and multiplying radical expressions using 2 examples you create.
Answer:
When you multiply radical expressions you multiply the numbers under the radical symbols.3–√×7–√=21−−√
When you add radical expression you CANNOT add the numbers under the radical symbols.
3–√+7–√≠10−−√
Step-by-step explanation:
India vs England test series in Nottingham
I will cheer for India because I am an Indian
Answer:
Is this suppose to be math question??
Answer:
hard work will define who wins
An office was built in the shape of a rectangle. If one side of the office measures 60 metres and the length is measured 4000 centimetres.
Calculate the perimeter of the office in meters.
Answer:
200m
Step-by-step explanation:
Width=60m
Length=4000cm=40m
[PERIMETER OF RECTANGLE= 2(l+b)]
2(40+60)
2×100
200cm
Two angels of a triangle are the same size.The third angel is 3 times as large as the first. How large are the angels
Answer:
Let the two equal angles be x . Hence the third angle is 3x . But the sum of the interior angles of a triangle always adds up to 180∘ . ∴x=1805=36∘
Answer:
Angle 1 = 36°
Angle 2 = 36°
Angle 3 = 108°
Step-by-step explanation:
Sum of all angles in any triangle is 180°
angle 1 = angle 2 = X
angle 3 = 3×X
angle 1 + angle 2 + angle 3 = 180°
X + X + 3×X = 5×X = 180°
X = 180° / 5 = 36°
Angle 1 = 36°
Angle 2 = 36°
Angle 3 = 108°
can someone help? Please
Answer: I can’t help with that because there should be a graph
Step-by-step explanation:
9) Determine which sides, if any, of the figures are parallel, perpendicular, or neither.
Rectangle BACD has coordinate B(-4,-3), A(-1, -7),C(3,-4), and D(0,0).
Answer:
Parallel: AC and DB, BA and CD
Perpendicular: AC and CD, DB and CD, DB and BA, BA and AC
Neither: None
Step-by-step explanation:
Step 1: Find Slopes
Let's first find the slopes of each side of the rectangle, as that will helps us determine which sides are parallel, perpendicular, or neither.
Recall that the formula for finding the slope between two points is [tex]\frac{y_2 - y_1}{x_2-x_1}[/tex] where [tex](x_1, y_1)[/tex] and [tex](x_2,y_2)[/tex] are the coordinates of the two points. To avoid confusion, I will be taking the first point I list as [tex](x_1,y_1)[/tex] and the second point as [tex](x_2,y_2)[/tex].
Slope of [tex]BA[/tex]:
[tex]\frac{-7-(-3)}{-1-(-4)}\\=\frac{-7+3}{-1+4} \\= -\frac{4}{3}[/tex]
Slope of [tex]AC[/tex]:
[tex]\frac{-4-(-7)}{3-(-1)} \\=\frac{-4+7}{3+1} \\=\frac{3}{4}[/tex]
Slope of [tex]CD[/tex]:
[tex]\frac{0-(-4)}{0-3} \\=\frac{4}{-3} \\=-\frac{4}{3}[/tex]
Slope of [tex]DB[/tex]:
[tex]\frac{-3-0}{-4-0} \\=\frac{-3}{-4} \\=\frac{3}{4}[/tex]
Step 2: Determine which sides are parallel, perpendicular, or neither
Now that we found the slopes of the sides, we can determine which sides are parallel, perpendicular, or neither.
Recall that parallel lines have the same slope. [tex]\bf AC[/tex] and [tex]\bf DB[/tex], along with [tex]\bf BA[/tex]and [tex]\bf CD[/tex], have the same slope, so they are parallel. No other pair of sides has the same slope, so these are our only parallel pairs.
For two lines to be perpendicular, the product of their slopes must be [tex]-1[/tex]. [tex]\bf AC[/tex] and [tex]\bf CD[/tex], [tex]\bf DB[/tex] and [tex]\bf CD[/tex], [tex]\bf DB[/tex] and [tex]\bf BA[/tex], and [tex]\bf BA[/tex] and [tex]\bf AC[/tex] [tex]\bf[/tex]meet that criteria, so they are perpendicular. No other pair of sides meets the criteria, so these are our only perpendicular pairs. Hope this helps!
What is the value of the rational expression below when x is equal to 3?
12 - x/X-6
A. 3
B. -3
C. 9
D. -9
Observe the below figure and answer.
Answer:
the answer is 5
Step-by-step explanation:
11 substract 6 is equal to 5
Identify a transformation of the function f(x) = x2 by observing the equation of the function g(x) = (x - 1)
Answer:
2nd option
Step-by-step explanation:
Given f(x) then f(x + a) is a horizontal translation of f(x)
• If a > 0 then a shift left of a units
• If a < 0 then a shift right of a units
Here g(x) = (x - 1)²
The base graph f(x) has been shifted right 1 unit
Use the quadratic formula to solve x² + 9x + 10 = 0.
What are the solutions to the equation?
Round irrational solutions to the nearest tenth.
(answer options):
Answer:
The quadratic formula: (-b+-sqrtb^2-4ac)/2a
Plugging in the values of a=1, b=9, and c=10, the roots of the equation are: -7.7 and -1.3.
So, the first option is correct.
Let me know if this helps!
What is the equation of the line represented by the table below?
Х
-2
-1
0
1
2
y
16
11
6
1
-4
O A. y = -5x+9
B. y = -3x - 5
O C. y = -5x + 3
D. y = -5x + 6
Answer:
D. y = -5x + 6
Step-by-step explanation:
If we replace the values of x in the expressions we can find y. By replacing the values of x we see that the only option that has the correct values of y is the option D.
HELP say im getting it wrong
the perimeter of the polygons is ?
solve for x.
solve for x.
solve for x.
Answer:
[tex]x=10[/tex]
Step-by-step explanation:
A secant is a line segment that intersects a circle in two places. One property of a secant is the product of the lengths ratio. This ratio can be described as the following, let ([tex]inside[/tex]) refer to the part of the secant that is inside the circle, and ([tex]outside[/tex]) refer to the part that is outside of it. ([tex]total[/tex]) will refer to the entirety of the secant or ([tex]inside+outside[/tex]). The numbers (1) and (2) will be used as subscripts to indicate that there are two different secants.
[tex](outside_1)(total_2)=(outside_2)(total_2)[/tex]
Substitute,
[tex](outside_1)(total_2)=(outside_2)(total_2)[/tex]
[tex](outside_1)(inside_1+outisde_1)=(outside_2)(inside_2+outside_2)[/tex]
[tex](6)(6+x+5)=(7)(7+x+1)[/tex]
Simplify,
[tex](6)(6+x+5)=(7)(7+x+1)[/tex]
[tex]6(x+11)=7(x+8)[/tex]
[tex]6x+66=7x+56[/tex]
Inverse operations,
[tex]6x+66=7x+56[/tex]
[tex]66=x+56[/tex]
[tex]10=x[/tex]
Find the length of each segment.
W X
Y
--5
0
5
5. WX
6. WY
The length of the line segments WX and XY will be 2 and 9, resprectively.
What is a line segment?A line segment in mathematics has two different points on it that define its boundaries. A line segment is sometimes referred to as a section of a path that joins two places.
The three points are W, X, and Y on the line.
From the diagram, the distance between the points W and X which is the line segment WX will be 2.
Similarly, from the diagram, the distance between the points W and Y which is the line segment WY will be 9.
More about the line segment link is given below.
https://brainly.com/question/25727583
#SPJ2
Helpppp please!!!!!!
Answer:
5/2
Step-by-step explanation:
tan&= 2/5(p/b)
here,
p=2,b=5
cot&=b/p
=5/2
I need help please I don't understand
Answer:
57.2
Step-by-step explanation:
This is a right triangle so we can use trig ratios.
We are asked to find a side when we know a angle adjacent to that side. And we are given a side opposite of that angle. We can use Tangent to find the side length.
[tex] \tan(40) = \frac{48}{x} [/tex]
Take the reciprocal of both sides.
[tex] \frac{1}{ \tan( 40) ) } = \frac{x}{ 48} [/tex]
Multiply both sides by 48.
[tex] x = \frac{1}{ \tan(40) } \times 48[/tex]
[tex]x = 57.2[/tex]
What is the length of the hypotenuse in the triangle below?
A right triangle is shown. 2 sides have lengths of 14 centimeters. The length of the hypotenuse is unknown.
a. 14 cm
b. 14 StartRoot 2 EndRoot cm
c. 14 StartRoot 3 EndRoot cm
d. 28 cm
Answer:
B
Step-by-step explanation:
Hypotenuse=sqrt(Side^2+side^2)=sqrt(14^2+14^2)=14*sqrt(2)
Answer:
B
Step-by-step explanation:
Hypotenuse=sqrt(Side^2+side^2)=sqrt(14^2+14^2)=14*sqrt(2)
FIRST ANSWER GETS BRAINLIEST!!
(sorry for the colors on the picture)
It is the 3rd answer
What is the measure of
Answer:
DEF = 105
Step-by-step explanation:
The sum of the angles of a triangle is 180
28+47+DEF = 180
Combine like terms
DEF+75=180
Subtract 75 from each side
DEF +75-75 =180-75
DEF = 105
Answer: D
Step-by-step explanation: The answer is D because firstly we know that all right triangles add up to 180 degrees.
Using this knowledge we know 2 sides out of the 3. Therefore 47+28+x=180. Then we would add the first 2 numbers then minus 180 to get 105 as your last angle.
