Answer:
ans: centre of circle is ( -4 , 6 )
and radius is 3 unit
Factorize x2 + 7x + 12 using middle term break method.
Answer:
(x + 4)(x + 3)
Step-by-step explanation:
x^2 + 7x + 12
In Quadratic Factorization using Splitting of Middle Term which is x term is the sum of two factors and product equal to last term. Factor each pair by finding common factors.
so we need two number that gives 12 when multiplied and 7 when added
4 and 3 are the numbers because 4*3 = 12 and 4+3 = 12
=x^2 + (4 + 3)x + 12
=x^2 + 4x + 3x + 12
=x(x + 4) + 3(x + 4)
take (x + 4) as common
=(x + 4) (x*1 + 3*1)
=(x + 4)(x + 3)
As an estimation we are told £3 is €4.
Convert €28 to pounds.
Hope this helps
Answer:
£21
€28 = £21
Abdi created a factor rainbow for the number 59.
Answer:
59 is prime ... 1 & 59 are the only factors
Step-by-step explanation:
..
What is the answer to this question?
Can someone help with this and help me understand this as well?
Answer:
<K ≅ <N
Step-by-step explanation:
JKL ≅ MNP
That means the angles are the same
<J ≅< M
<K ≅ <N
<L ≅<P
The sides are also congruent
JK ≅ MN
KL ≅ NP
JL ≅ MP
PLEASE ANSWER ASAP
expand and simplify the following:
a) (√6+√3)(√6-√3) b)(√5-√2)(√2+√5)
Answer:
[tex]{ \bf{a).}} \\ { \tt{( \sqrt{6} + \sqrt{3} )( \sqrt{6} - \sqrt{3}) }} \\ { \tt{ = ( { \sqrt{6} )}^{2} - {( \sqrt{3}) }^{2} }} \\ { \tt{ = 6 - 3}} \\ { \tt{ = 3}} \\ \\ { \bf{b).}} \\ { \tt{( \sqrt{5} - \sqrt{2})( \sqrt{2} + \sqrt{5} )}} \\ { \tt{ = ( { \sqrt{5} }^{2}) - { (\sqrt{2} }^{2}) }} \\ { \tt{ = 5 - 2}} \\ { \tt{ = 3}}[/tex]
Answer:
(6-3)(5-2)=3×3=9
Step-by-step explanation:
[tex]x ^{2} - {y}^{2} = (x - y)(x + y)[/tex]
[tex]( \sqrt{6} - \sqrt{3} )( \sqrt{6} + \sqrt{3} ) = ( { \sqrt{6} }^{2} - { \sqrt{3} }^{2} ) = 6 - 3 = 3[/tex]
the sum of ages of two brothers A and B is 35 A is two thirds of B's age find their ages
Answer:
let the ages of the brothers be 2x and 3x
2x +3x=35
5x=35
x=35÷5
x=7
now,
A=2x=2×7=14
B=3x=3×7=21
this is the answer
The three angles in a triangle have measures of 55°, 75°, and (2x)°. What is the value of x?
Answer:
x = 25
Step-by-step explanation:
The angles in a triangle add up to 180°, so we can write an equation to model the situation:
55 + 75 + 2x = 180
Now, we can simplify and solve:
130 + 2x = 180
2x = 50
x = 25
Answer:
x = 25
Step-by-step explanation:
The angles in a triangle add up to 180 degrees.
Using this, create an equation:
55 + 75 + 2x = 180
Solve for x:
55 + 75 + 2x = 180
130 + 2x = 180
2x = 50
x = 25
So, x = 25
please help it asks: the graph below represents which of the following functions
Help pls I'll give 25 points
Answer:
[tex]\text{C. }60[/tex]
Step-by-step explanation:
Question from image:
"The digits 1, 2, 3, 4, and 5 can be formed to arrange 120 different numbers. How many of these numbers will have the digits 1 and 2 in increasing order? For example, 14352 and 51234 are two such numbers."
Let's start by taking a look with the number 1. There are four possible places 1 could be, because there needs to be space for the 2 after it.
Checkmarks mark where the 1 can be, the x marks where it cannot be.
[tex]\underline{\checkmark}\:\underline{\checkmark}\:\underline{\checkmark}\:\underline{\checkmark}\:\underline{X}[/tex]
Let's start with the first position:
[tex]\underline{\checkmark}\:\underline{\#}\:\underline{\#}\:\underline{\#}\:\underline{\#}[/tex]
There are four places the 2 can be. For each of these four places, we can arrange the remaining 3 digits in [tex]3!=6[/tex] ways. Therefore, there are [tex]4\cdot 6=\boxed{24}[/tex] possible numbers when 1 is the first digit of the number.
Continue this process with the remaining possible positions for 1.
Second position:
[tex]\underline{X}\underline{\checkmark}\:\underline{\#}\:\underline{\#}\:\underline{\#}[/tex]
There are three places the 2 can be, since the 2 must be behind the 1. For each of these three places, the remaining 3 digits can be arranged in [tex]3!=6[/tex] ways. Therefore, there are [tex]3\cdot 6=\boxed{18}[/tex] possible numbers when 1 is the second digit of the number.
The pattern continues. Next there will be 2 places to place the 2. For each of these, there are [tex]3!=6[/tex] ways to rearrange the remaining 3 digits for a total of [tex]2\cdot 6=\boxed{12}[/tex] possible numbers when 1 is the third digit of the number.
Lastly, when 1 is the fourth digit of the number, there is only 1 place the 2 can be. For this one place, there are still [tex]3!=6[/tex] ways to rearrange the remaining three numbers. Therefore, there are [tex]1\cdot 6=\boxed{6}[/tex] possible numbers when 1 is the fourth digit of the number.
Thus, there are [tex]24+18+12+6=\boxed{60}[/tex] numbers that will have the digits 1 and 2 in increasing order, from a set of 120 five-digit numbers created by the digits 1 through 5, where no digit may be repeated.
Mark 4/9 and -7/9 on a number line.
Answer:
Step-by-step explanation:
4/9 on the number line would be 0.44.
-7/9 on the number line would be -0.77
Choose which group of measures would go along with the data set below.
11,13,11,9,8,4,7,7,11,9
1.
Range—4
Mode—8
Median—9
Mean—9
2.
Range—5
Mode—9
Median—7
Mean—7
3.
Range—9
Mode—11
Median—9
Mean—9
4.
Range—12
Mode—8
Median—9
Mean—9
Which are solutions to the system of equations? Select all that apply
{y=4x
y=4x^2+4x-1
A (1/2,2)
B.(-1/4,-1)
C. (-1/2,-2)
D. (1/4,1)
Answer:
A, C are both solutions
Step-by-step explanation:
B will not work because:
-1 = 4(-1/4)² + 4(-1/4) - 1
-1 = 1/4 - 1 - 1
-1 ≠ -1 3/4
D will not work because:
1 = 4(1/4)² + 4(1/4) - 1
1 = 1/4 + 1 - 1
1 ≠ 1/4
Student pick 144 oz of strawberry to make strawberry jam how many ounce pounds of strawberry did they pick
Answer:
9 pounds
Step-by-step explanation:
1 lb = 16 ounces
144/16 = 9 pounds
mmmmm hey can you explain my math?
Answer:On June 17
the explanation is in the picture
In the diagram below, AB = BC, and mZA = 69º. Find mZBCD.
Answer:
∠ BCD = 111°
Step-by-step explanation:
Since AB = BC then the triangle is isosceles and the 2 base angles are congruent.
∠ ACB = ∠ A = 69°
∠ ACB and ∠ BCD are adjacent angles and sum to 180° , that is
∠ BCD + ∠ ACB = 180°
∠ BCD + 69° = 180° ( subtract 69° from both sides )
∠ BCD = 111°
Please give real answers with explaination. 50 points + I will give brainliest. No Docs/No Files/No Links only answer with explaination.
Answer:
Step-by-step explanation:
That exterior angle is equal to the sum of the remote interiors, specifically:
2x + 3 = 45 + x + 8 and
x = 50
So the angles inside the triangle...we already know one of them is 45. If x = 50, then x + 8 is 50 + 8 = 58. That means that the third angle is 180 - 45 - 58 which is 77.
Solve the following system of equations.
\begin{aligned} -5x+4y &= 3\\\\ x&=2y-15 \end{aligned}
−5x+4y
x
=3
=2y−15
x=?
y=?
Step-by-step explanation:
The first president of the United States was
[tex]\begin{aligned} -5x+4y &= 3\\\\ x&=2y-15 \end{aligned}[/tex]
Answer:
x=9
y=12
Step-by-step explanation:
In 2 Year 6 classes, 2/5 of the children are girls. There are 39 boys. How many children are there in the class?
Pls help
An airplane can Seat up to 175 passengers the airplane has already sold 87 tickets for a flight on the airplane which graph represents the solution to the inequality that find a number of tickets the air line can still sell
Answer:
the third graph is the answer
Answer:
It's A.
Step-by-step explanation:
Since 175-87 is 88, there is 88 or less available tickets left. So it is A.
Hope this helps.
please help i will give brainliest
Step-by-step explanation:
4(2.8*4.5)=50.4
50.4/12= 4.2
4.2 means 5 tins of paint
£52.5 =price
Step-by-step explanation:
i have explained in the paper.
Goodluck
Please Helppp!! 50 Points
Compute the sum
10235
I just typed it in a calculator
the answer is in the above image
Answer:
Step-by-step explanation:
5* (2⁰ + 2¹ + 2 ²+ 2³+ ........+ 2¹⁰)
Sum of geometric series = [tex]a*\frac{r^{n}-1}{r-1}[/tex]
a -> first term = 1
r- ratio = 2
n --> number of terms = 11
5* (2⁰ + 2¹ + 2 ²+ 2³+ ........+ 2¹⁰)=
[tex]5*[1*\frac{2^{11}-1}{2-1}]\\\\=5 *[1*(2048-1)]\\\\= 5 * 2047\\= 10235[/tex]
The weight Wkg of a metal bar varies jointly as it's length L and the square of it's diameter D mm. If W=140 when D =4 and L=54, find D interm of W and L
Answer:
D = [tex]\sqrt{\frac{216W}{35L} }[/tex]
Step-by-step explanation:
From the given question, the expression showing the relationship among the weight, length and diameter of the metal bar is;
W [tex]\alpha[/tex] L[tex]D^{2}[/tex]
W = kL[tex]D^{2}[/tex]
where k is the constant of proportionality.
When W = 140, D = 4 and L = 54, then;
140 = k(54)[tex](4)^{2}[/tex]
= 864k
k = [tex]\frac{140}{864}[/tex]
= [tex]\frac{35}{216}[/tex]
k = [tex]\frac{35}{216}[/tex]
⇒ W = [tex]\frac{35LD^{2} }{216}[/tex]
So that;
35L[tex]D^{2}[/tex] = 216W
[tex]D^{2}[/tex] = [tex]\frac{216W}{35L}[/tex]
D = [tex]\sqrt{\frac{216W}{35L} }[/tex]
Help ASAP!!!!!!!!!!!!!!
There is a bag filled with 5 blue and 6 red marbles.
Marble is taken at random from the bag, the colour is noted and then it is replaced.
Another marble is taken at random.
What is the probability of getting 2 reds?
thanks,
Answer:
[tex](\frac{6}{11} )*(\frac{6}{11} )[/tex] = 36/121 =.297
Step-by-step explanation:
Answer:
36/121
Step-by-step explanation:
We have 5+6 = 11 marbles
P(red) = number of red/ total = 6/11
We replace the marble so we still have 11 marbles
P(red) = number of red/ total = 6/11
P(red, red) = 6/11*6/11 = 36/121
6 root20+8 root5-5root45
Answer:
Step-by-step explanation:
[tex]6\sqrt{20} + 8\sqrt{5} -5\sqrt{45}[/tex]
[tex]12\sqrt{5} + 8\sqrt{5} -15\sqrt{5}[/tex]
[tex]5\sqrt{5}[/tex]
Answer:
Step-by-step explanation:
I imagine that you are simplifying this, since there is nothing else you can do with it. You are in the section in algebra where you're learning how to simplify radicals. ALWAYS think prime factorization when it comes to numbers. For example, the square root of 5...the prime factorization of 5 is simply 5 * 1. So we know that √5 is as simple as it can be. It would benefit us if we could simplify either of the other 2 radicals down to the same radicand so we could add or subtract them.
The prime factorization of 20 is
20--> 5 * 4
4--> perfect square (2×2). So the simplification of 6√20 is 6×2√5 which is 12√5.
The prime factorization of 45 is
45--> 5 * 9
9--> perfect square (3×3). So the simplification of 5√45 is 5×3√5 which is 15√5.
Put it all together to get
12√5 + 8√5 -15√5 which simplifies to
5√5
One piece of wood has a rectangular bottom that is 30 cm long and 56 mm wide. The block is said to weigh 80 N. Calculate the pressure that the block exerts on the surface
Answer:
4762 N/m^2
Step-by-step explanation:
Find area.
30x5.6=168
Convert to m^2
168cm^2=0.0168m^2
Use pressure formula to get answer
P=F/A
P=80/0.0168
P=4762 N/m^2
Which is equivalent to (square root 10) ^3/4?
Answer:
2nd option
Step-by-step explanation:
Using the rule of exponents/ radicals
[tex]a^{\frac{m}{n} }[/tex] ⇔ [tex](\sqrt[n]{a}) ^{m}[/tex] , then
[tex]\sqrt{10} ^{\frac{3x}{4} }[/tex]
= [tex](\sqrt[4]{10}) ^{3x}[/tex]
The distance required to stop a car varies directly as the square of its speed.if 250 feet are required to stop a car traveling 60 miles per hour, how many feet are required to stop a car traveling 96miles per hour
Answer:
640 feet.
Step-by-step explanation:
Let d represent the distance required to stop and let s represent the speed of the car.
The distance required to stop varies directly as the square of its speed. In other words:
[tex]d=ks^2[/tex]
Where k is the constant of variation.
250 feet are required to stop a car traveling 60 miles per hour. Substitute:
[tex](250)=k(60)^2[/tex]
Simplify and solve for k:
[tex]\displaystyle 3600k=250\Rightarrow k=\frac{250}{3600}=\frac{25}{360}=\frac{5}{72}[/tex]
So, our equation is:
[tex]\displaystyle d=\frac{5}{72}s^2[/tex]
Then the distance required to stop a car traveling 96 miles per hour will be:
[tex]\displaystyle d=\frac{5}{72}(96)^2=\frac{5}{72}(9216)=640\text{ feet}[/tex]
Does anyone know the answer??
Answer:
175°
Step-by-step explanation:
If angle x = 058° and angle y = 127° then the bearing A from point O is 360 minus angle x plus angle y.
Solution:
360° - (058° + 127°) = 175°
This is because the complete turn from north to north is 360°.