Answer:
-5 <x<-1
Step-by-step explanation:
4|x+3|<8
Divide by 4
4|x+3| /4<8/4
|x+3|<2
There are two solutions one positive and one negative, remember to flip the inequality for the negative
x+3 <2 and x+3 >-2
Subtract 3 from each side
x+3-3 <2-3 and x+3-3 >-2-3
x<-1 and x>-5
-5 <x<-1
Elliot is 2 times as old as Tanya. 10 years ago, Elliot was 4 times as old as Tanya. How old is Elliot now?
Answer:
Step-by-step explanation:
To solve this, we are going to make an age table:
Age Now Age 10 years ago
Tanya
Elliot
Filling the in the Age Now column comes from the first sentence. If Elliot is 2 times Tanya's age and we don't know Tanya's age, then Tanya's age is x and Elliot's age is 2x:
Age Now Age 10 years ago
Tanya x
Elliot 2x
Filling in the Age 10 years ago column simply requires that we take their ages in the Age Now column and subtract 10 from each age:
Age Now Age 10 years ago
Tanya x x - 10
Elliot 2x 2x - 10
Since the question is How old is Elliot now based on the fact that 10 years ago....blah, blah, blah, we are using the ages in the 10 years ago column to write our equation. It says:
10 years ago, Elliot was 4 times as old as Tanya. Translated into mathspeak:
2x - 10 = 4(x - 10) and
2x - 10 = 4x - 40 and
-2x = -30 so
x = 15. That means that Elliot is 30 and Tanya is 15
Please show your work
[tex]1\frac{2}{3} + 2\frac{3}{4}[/tex]
Answer:
[tex]→1 \frac{2}{3} + 2 \frac{3}{4} \\ = \frac{5}{3} + \frac{11}{4} \\ = \frac{20 + 33}{12} \\ = \frac{53}{12}\\ =\boxed{4\frac{5}{12}}✓[/tex]
53/12 is the right answer.Steps:
1 2/3 + 2 3/4 can also be written as...
5/3 + 11/4
The LCD is 12 so we make both fractions have a denominator of 12.
That gives us 20/12+33/12
Now you can add the numerators (but leave the denominator the same)
That gives us 53/12, but our simplified version would give us 4 5/12 as our final answer.
Answer:
[tex]4\frac{5}{12\\}[/tex]
Please mark brainliest if that helps!
ILL GIVE POINTS!!
Suppose a triangle has two sides of length 3 and 4 and that the angle
between these two sides is pi/3 What is the length of the third side of the
triangle?
A. sqrt13
B. 4sqrt3
C. sqrt3
D. 3
Answer:
no A
Step-by-step explanation:
sqrt13 is the ans
hope it helps
Prove that 1/√2 is irrational
Answer:
Step-by-step explanation:
Let's assume that it is rational , so this number can be represented as[tex]\Large \boldsymbol{}\bf \dfrac{p^{^/is \ an \ integer}}{q^{ / natural}} -irreducible \ \ fraction[/tex]
[tex]\Large \boldsymbol{}\bf \dfrac{1 ^{/ an \ integer }}{\sqrt{2}^{ / not \ \ integer } }[/tex] -Since the denominator is not a natural number then the 1/√2 is respectively an irrational number
4. Which property of similarity can be used to prove triangles DEF and GHI are similar?
Answer:
SSS
Step-by-step explanation:
We know all three sides of both triangles. The common ratio of DEF to GHI is 2/3.
Answer:
SSS
Step-by-step explanation:
Similar triangles must have congruent corresponding angles and proportional corresponding sides.
This equation shows how the total number of necklaces Denise owns is related to the amount of money she spends on additional necklaces.
n = d + 74
The variable d represents the amount of money she spends on additional necklaces, and the variable n represents the total number of necklaces she owns. With $16 to spend on new necklaces, how many total necklaces can Denise own?
Answer:
16+74
Step-by-step explanation:
substitute 16 into the equation
Can anyone help plz?
Answer:
just add a small amount and and square the new number
between 2.82 and 2.83 seems a bit closer
Step-by-step explanation:
x x^2
2.8 7.84
2.81 7.8961
2.82 7.9524
2.83 8.0089
2.84 8.0656
2.85 8.1225
2.86 8.1796
2.87 8.2369
Another of Bhaskara's problems results in a quadratic equation Parthava was enraged and seized a certain number of arrows to slay Karna. He expended one-half of them in defending himself. Four times the square root of the number of arrows were discharged against the horses. With six more, he transfixed Shalya, the charioteer. With three more, he rent the parasol, the standard, and the bow; and with the last one he pierced the head of Karna. How many arrows did Parthava have?
Answer:
Parthava had 100 arrows.
Step-by-step explanation:
Let's define N as the number of arrows that Parthava originally has.
He uses one-half of them in defending himself, so he used N/2 arrows
Now he uses four times the square root of the number of arrows, so now he uses:
4*√N
Then he uses 6
Then he uses 3
Then he uses the last one.
If we add all these numbers of arrows that he used, we should get the initial number of arrows that he used, then:
N/2 + 4*√N + 6 + 3 + 1 = N
Now we have an equation that we can try to solve.
First, let's move all the terms to the same side:
N/2 + 4*√N + 6 + 3 + 1 - N = 0
now we can simpify it:
(N/2 - N) + 4*√N + (6 + 3 + 1) = 0
-(1/2)*N + 4*√N + 10 = 0
Now we can define a new variable x = √N
Then we have: x^2 = N
now we can replace these new variables in our equation to get:
-(1/2)*x^2 + 4*x + 10 = 0
Now we just have a quadratic equation.
Remember that for a quadratic equation of the form:
0 = a*x^2 + b*x + c
The solutions were given by:
[tex]x = \frac{-b \pm \sqrt{b^2 - 4*a*c} }{2a}[/tex]
Then in our case, the solutions will be:
[tex]x = \frac{-4 \pm \sqrt{4^2 - 4*(-1/2)*10} }{2*(-1/2)} = \frac{-4 \pm 6 }{-1} = 4 \pm 6[/tex]
So there are two solutions:
x = 4 + 6 = 10
x = 4 - 6 = -2
And remember that x = √N
Then x should be positive, then we take x = 10 as our solution here.
then we can use the equation:
x = 10 = √N
then
10^2 = √N^2 = N
10^2 = 100 = N
Parthava had 100 arrows.
Triangles and angles
Pls help
Answer:
The two bottom angles of this triangle are both represented by the same variable, in this case, an x. This means, that both of the bottom angles are equal to each other.
So we have:
32 + x + x = 180 (since the TOTAL angles of a triangle adds up to 180)
32 + 2x = 180 (combine the 2 x's together)
2x = 148 (subtract a 32 from both sides)
x = 74
Let me know if this helps!
Find the missing value.
Hint: Use the number line to find the missing value.
了。
-(-2)
{
开
-10
-5
→
15
0
5
10
-15
Answer:
-5
Step-by-step explanation:
-5 -(-2)
=-7
I hope this helped!Convert 5π∕6 radians to degrees. Question 1 options: A) 25° B) 150° C) 150π° D) 1080°
Step-by-step explanation:
Hi there!
Given;
= 5(π\6)
We have;
π = 180°
Keeping value of π in the question;
= 5(180°/6)
= 5*30°
= 150°
Therefore, answer is option B.
Hope it helps!
Can someone help me on this math question its confusing ill give brainly when right!!!
Answer:
x=5
Step-by-step explanation:
x=[tex]\sqrt{25}[/tex]
x=5
which choice is equivalent to the expression below? 7x√2 - 4√2 + x√2
A. 6x√2 - 3√2
B. 5x^2√2
C. 3x√2
D. 8x√2 - 4√2
Answer:
D
Step-by-step explanation:
[tex]8x \sqrt{2} - 4 \sqrt{2} [/tex]
Find C to two decimal places and find the measurement of angle be use your calculator
Let's solve
P=8B=5Using Pythagorean theorem
[tex]\\ \sf\longmapsto H^2=P^2+B^2[/tex]
[tex]\\ \sf\longmapsto c^2=8^2+5^2[/tex]
[tex]\\ \sf\longmapsto c^2=64+25[/tex]
[tex]\\ \sf\longmapsto c^2=89[/tex]
[tex]\\ \sf\longmapsto c=\sqrt{89}[/tex]
[tex]\\ \sf\longmapsto c\approx 9.22[/tex]
Drag the tiles to the boxes to form correct pairs. Not all tiles will be used. Match each set of vertices with the type of quadrilateral they form.
I'm sorry but there's not enough info
Step-by-step explanation:
Answer:
The triangle with vertices A (2 , 0) , B (3 , 2) , C (5 , 1) is isosceles right Δ
The triangle with vertices A (-3 , 1) , B (-3 , 4) , C (-1 , 1) is right Δ
The triangle with vertices A (-5 , 2) , B (-4 , 4) , C (-2 , 2) is acute scalene Δ
The triangle with vertices A (-4 , 2) , B (-2 , 4) , C (-1 , 4) is obtuse scalene Δ
calculate the speed, in ms-¹ of vehicle A and of vehicle B
9514 1404 393
Answer:
A: 0.32 m/sB: 0.56 m/sStep-by-step explanation:
The speed is the ratio of the change in distance to the corresponding change in time.
Vehicle A moves from a position of 12 m to one of 28 m in 50 seconds, so its speed is ...
A = (28 -12)/50 m/s = 16/50 m/s = 0.32 m/s
Vehicle B moves from 0 to 28 m in 50 seconds, so its speed is ...
B = (28 m)/(50 s) = 0.56 m/s
Can someone please help me with these 4 questions?
Which of the following have a total of 8 possible outcomes? Check all that apply.
Answer:
Probably the first three answers
Step-by-step explanation:
The rest are
4) 3×5=15 (which is not 8)
5) 6×2=12 (≠8)
So it's just the first three
find the vertex of this parabola y=-2x ^2-4x-5
Answer:
(1, -13)
Brainliest, please!
Step-by-step explanation:
To find the x coordinate of the vertex, we use the formula, -b / 2a. In this problem, a = 2, and b = -4. c is -5, but we don't need to know it.
- -4 / 2(2) = 4 / 4 = 1
Vertex = (1, y)
Next, we plug 1 back into the parabola equation for x to solve for y.
y = -2(1)^2 - 4(1) -5
y = -2^2 - 4 - 5
y = -4 - 4 - 5
y = -8 - 5
y = - 13
Vertex = (1, -13)
If a school camp has enough food for 150 students over 5 days
How long would the food last for is only 100 students are there
Answer:
It is over 7 days
hope it helps
PLEASE HELP!!!!!!!
Which terms are like terms in the following expression? 3x + 3xy – 2x + 5y + 5x2
A. 3x and -2x
B. 3x, -2x and 5x2
C. 3x, 3xy, -2x and 5y
D. All terms are alike.
Answer:
C
Step-by-step explanation:
please answer this question!!
Answer:
a
Step-by-step explanation:
all angles of an equilaterall triangle are equal therefore 180÷3 = 60
The library has 2,730 books. If each shelf can hold 30 books, how many shelves will the library need to hold all of its books?
Answer:
2730÷30=91
Step-by-step explanation:
take the number of books and divide it by the number of books each shelve can hold and ull get ur answer
Rob cuts a circular hole out of a rectangular piece of paper. The paper measures 20 centimeters by 30 centimeters. The hole is 10 centimeters in diameter. How much of the piece of paper, in square centimeters, is left over after the hole is cut out?
Answer:
521.25
Step-by-step explanation:
the circle is 78.75 in area and the square is 600 so 600- 78.75 = 521.25
15. Mary was given data comparing students’ mark in math class and the number of classes missed. She plotted the data on the graph below and drew a line of best fit. Do you agree with Mary’s drawing of the line of best fit? Justify your answer
traders fix the price of cosmetic items 30% above the cost price when he sold an item at 25% discount there was a loss of Rs 15 find the cost price and marked price of the item
Cost price is Rs600 and marked price is Rs780.
Must click thanks and mark brainliest
ASAP !
Determine the value of x.
Question 1 options:
A: x = 2
B: x = 2.5
C: x = 1
D: x = 2.9
Answer:
x=2
Step-by-step explanation:
We can use the Pythagorean theorem since this makes a right triangle
a^2+b^2 = c^2
The radius is 1.5
1.5^2 + x^2 = (1+1.5)^2
1.5^2 +x^2 = 2.5^2
2.25+x^2=6.25
Subtract 2.25 from each side
x^2 = 4
Taking the square root of each side
x= 2
Answer:A
Step-by-step explanation:Took quiz
[tex](32)^{1/5}[/tex]
Answer:
2Step-by-step explanation:
[tex] {32}^{ \frac{1}{5} } [/tex]
[tex] = \sqrt[5]{32} [/tex]
[tex] = \sqrt[5]{2 \times 2 \times 2 \times 2 \times 2} [/tex]
= 2 (Ans)
The temperature on a mountain peak was 7 degreesFahrenheit (F) at 6:00 p.m. By 8:00 p.m., thetemperature had dropped to 0F. If the temperaturecontinued to drop at about the same rate, which isthebestestimate of the temperature at 11:00 p.m
A -20 / B. -14 / C -10 / D -9 /
Given:
The temperature on a mountain peak was 7°F at 6:00 p.m.
By 8:00 p.m., the temperature had dropped to 0°F.
To find:
The temperature at 11:00 p.m. if the temperature continued to drop at about the same rate.
Solution:
Time between 6:00 p.m. to 8:00 p.m. is 2 hours.
Change in temperature in 2 hours is -7°F.
Change in temperature in 1 hours is [tex]-\dfrac{7}{2}^\circ[/tex]F.
Time between 8:00 p.m. to 11:00 p.m. is 3 hours.
Change in temperature in 3 hours is [tex]3\times \dfrac{-7}{2}^\circ[/tex]F, i.e., [tex]-\dfrac{21}{2}^\circ[/tex]F.
Now, the temperature at 11:00 p.m is:
[tex]0-\dfrac{21}{2}=-10.5[/tex]
Therefore, the temperature at 11:00 p.m. is -10.5°F.
Note: All options are incorrect.
To paint a wooden cube, Pinocchio needs 4 grams of paint. When it is dry, he cut the cube into 8 smaller pieces of smaller size. How much paint additional paint does Pinocchio need to paint the unpainted surfaces of the smaller cubes
Answer:
9 grams of paint
Step-by-step explanation:
6×8=48
48÷4= 12
48-12=36
36÷4=9
first multiply 6 by 8 because a cube has six faces and you cut that cube eight times
second after you cut that you will have 48 faces and for every six faces there are 4 grams of paint so you divide 48 by 4 and you get 12 this means that 12 of the faces are painted
next you subtract 12 from 48 and you get 36 this means that 36 faces are not painted
lastly you divide 36 by 4 and you will get 9 grams of paint
