Answer:
(x + 7)(x - 3)
Step-by-step explanation:
To factor the quadratic
Consider the factors of the constant term (- 21) which sum to give the coefficient of the x- term (+ 4 )
The factors are + 7 and - 3 since
+ 7 × - 3 = - 21 and + 7 - 3 = + 4, hence
x² + 4x - 21 = (x + 7)(x - 3)
The quadratic equation x^2 + 4x - 21 is factored into (x - 3)(x + 7) where these two factors multiply to -21 and add up to 4.
Explanation:To completely factor the equation x^2 + 4x - 21, we look for two numbers that multiply to -21 (the c term) and add up to 4 (the b term). The numbers that satisfy these conditions are 7 and -3.
Therefore, the factored form of the equation x^2 + 4x - 21 is: (x - 3)(x + 7) as (x - 3) * (x + 7) gives x^2 + 4x - 21.
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Find the length of the side of a square with an area of 49.
A. 49
B. 7
C. 25
D. 2,401
7 is the answer
Area =length *breadth
Area =length *length
Area=49=x *x
[tex]49 = {x}^{2} \\ \sqrt{49} = x \\ x = 7[/tex]
need urgent help asap! trig question 7, 9, 10, 11, 12plz,, plz show step by step work on each one plz!
You just need a calculator for these so there is no working
7)[tex]4.569245397*10^{-3}[/tex]
8)[tex]\frac{1}{2}[/tex]
9)0.5773502692
10)[tex]6.853838284*10^{-3}[/tex]
I am not sure for the rest, sorry havent done that far in school yet :)
Hope these helps :)
You need the Unit Circle to answer these questions! (attached)
7. Answer: [tex]\bold{\dfrac{\sqrt6-\sqrt2}{4}}[/tex]
Step-by-step explanation:
[tex]sin\dfrac{\pi}{12}=15^o\\\\\text{Since }15^o\text{ is not on the Unit Circle, you will need to use the difference}\\\text{formula for sin: sin(A - B) = sinAcosB - cosAsinB}\\\\sin15=sin(45-30)=\dfrac{\sqrt2}{2}\cdot\dfrac{\sqrt3}{2}-\dfrac{\sqrt2}{2}\cdot\dfrac{1}{2}=\dfrac{\sqrt6}{4}-\dfrac{\sqrt2}{4}=\boxed{\dfrac{\sqrt6-\sqrt2}{4}}[/tex]
8. Answer: 0
Step-by-step explanation:
The sum formula for cos is: cos (A + B) = cosA cosB - sinA sinB
Since we are given cos75° cos15° - sin75° sin15°, we can conclude that we are looking for cos (75° + 15°) = cos 90°.
The Unit Circle shows us that cos 90° = 0
9. Answer: [tex]\bold{\dfrac{\sqrt3}{3}}[/tex]
Step-by-step explanation:
The given expression is for tan (A + B).
tan (10° + 20°) = tan 30° = [tex]\dfrac{sin30^o}{cos30^o}=\dfrac{1}{\sqrt3}\implies\boxed{\dfrac{\sqrt3}{3}}[/tex]
10. Answer: [tex]\bold{\pm\dfrac{2-\sqrt2}{2}}[/tex]
Step-by-step explanation:
[tex]sin\dfrac{\pi}{8}=22.5^o=sin\dfrac{45^o}{2}\\\text{So we need to use the half-angle formula for sin:}\\\\sin\dfrac{\theta}{2}=\pm\sqrt\dfrac{1-cos\theta}{2}}\\\\sin\dfrac{45^o}{2}=\pm\sqrt\dfrac{1-cos45^o}{2}}=\pm\sqrt\dfrac{1-\frac{\sqrt2}{2}}{2}}=\pm\sqrt\dfrac{\frac{2}{2}-\frac{\sqrt2}{2}}{\frac{4}{2}}}=\boxed{\pm\dfrac{2-\sqrt2}{2}}[/tex]
11. TOO BLURRY TO SEE THE PROBLEM
12. Answer: [tex]\bold{\dfrac{7}{25}}[/tex]
Step-by-step explanation:
Quadrant II means that sin is positive and cos is negative.
[tex]sin\ x=\dfrac{3}{5}\implies cos\ x=-\dfrac{4}{5}\\\\cos\ 2x=cos^2\ x-sin^2\ x\\\\.\qquad=\bigg(\dfrac{-4}{5}\bigg)^2-\bigg(\dfrac{3}{5}\bigg)^2\\\\.\qquad=\dfrac{16}{25}-\dfrac{9}{25}\\\\.\qquad=\boxed{\dfrac{7}{25}}[/tex]
I need help please ..
Answer: The correct answer is C
Step-by-step explanation: since the 8 has a less than or equal too sign the bubble will be filled, and since the 6 has just a greater than sign the bubble is left empty. Also all the numbers are postive so the line would be on the postive side of the line graph.
Find the surface area of the rectangular prism
Answer:
S.A. = 328Step-by-step explanation:
The formula of a surface area of a rectangular prism l × w × h:
[tex]S.A.=2(lw+ih+wh)[/tex]
We have l = 5.5, w = 5 and h = 13. Substitute:
[tex]S.A.=2(5.5\cdot5+5.5\cdot13+5\cdot13)\\\\S.A.=2(27.5+71.5+65)\\\\S.A.=2(164)\\\\S.A.=328[/tex]
If the greatest value of n is 8, which inequality best shows all the possible values of n? (5 points) n < 8 n ≤ 8 n > 8 n ≥ 8
Answer:
Step-by-step explanation:
"the greatest value of n is 8" is signified by n ≤ 8.
This is a set, and also an inequality.
Brenda walk the dogs after school she is planning to increase the rate that she charges by 20% in January when does current rate for walking a dog is $4.50 what will be the new rate in dollars after the 20% increase? Plz show work
Answer:
$5.40
Step-by-step explanation:
To find the increase we need to consider our variables.
Current Rate = $4.50
Increase Percentage = 20% or 0.20
Now we can find the new rate by multiplying the Current Rate to the Increase Percentage and add it to the Current Rate again.
Total Price w/ Increase = ($4.50 x 0.20) + $4.50
Total Price w/ Increase = $0.90 + $4.50
Total Price w/ Increase = $5.40
{System: I am having a bit of trouble calculating this. Will you help me out? Thank you!}
what is the greatest number of roots a polynomial of degree 15 can have ?
Answer:
15
Step-by-step explanation:
The highest exponent in a polynomial function is the degree. The degree is also the greatest number of roots available. Since roots come from the factors of the function, as each factor is multiplied the degree increases. If the degree is 15 the greatest number of factors or roots it can have is 15.
Find the volume of the solid figure 3’width 5’length and 6’height
A:90 cu. ft
B:96 cu. ft
C:126 cu. ft
Volume=length×width×height
=5×3×6
=90 cu.ft
Answer:
A. 90 cu.ftStep-by-step explanation:
The formula of a volume of a rectangular solid (cuboid):
[tex]V=lwh[/tex]
l - length
w - width
h - height
We have
[tex]l=5\ ft,\ w=3\ ft,\ h=6\ ft[/tex]
Substitute:
[tex]V=(5)(3)(6)=90\ ft^3[/tex]
Which of the following is written in correct scientific notation? 52.6 * 10-9 6.39 * 109 0.12 * 10-2 10 * 107
Answer:
Step-by-step explanation:
I will take a to be 52.6 * 10^-9 The number should be 5.26 * 10^-8 so A is not the answer.
6.39*10^9 This one is correct.
0.12 * 10^-2 is not correct. It should be 1.2*10^-3
10 * 10 ^7 should be 1*10^8 so D is not correct.
The coefficient of scientific notation must be a number between 1 and 10 and including 1 but not 10. This is written as 1 ≤x <10
Final answer:
To determine if a number is written in correct scientific notation, it must have a coefficient between 1 and 10, followed by 'x 10' raised to an exponent. For the options provided, the number 6.39 × 10⁹ fits the proper scientific notation format.
Explanation:
To be written in correct scientific notation, a number must be in the form of a single non-zero digit followed by a decimal and any subsequent digits, times a power of ten. Here are the requirements for correct scientific notation:
The numerical part (coefficient) must be a number greater than or equal to 1 and less than 10.We then follow by 'x 10' raised to an exponent (power) that is an integer.Let's evaluate the provided options and convert them to correct scientific notation if needed:
72.44 × 10³ should be 7.244 × 10⁴9,943 × 10⁻⁵ should be 9.943 × 10⁴588,399 × 10² should be 5.88399 × 10⁵The number in correct scientific notation from the initial options given is 6.39 × 10⁹
D(1, 1), E(1,−2), F(−2,−2), G(−2, 1) The perimeter of the figure is a units.
Answer:
9 units squared
Step-by-step explanation:
The figure is a rectangle with length 3 and height 3. See attached picture. The area is found using A = b*h = 3*3 = 9.
the number that is 3 times the sum 5 and 7 i wrote 3 x 5 + 7 explain why i cannot use this expression to find the number
Answer:
3X(5+7)
Step-by-step explanation:
Because correctly is of this way:
3X(5+7)
and not so:
(3X5) + 7
Best regards
➷ You have written it the incorrect way.
Following the rules of PEMDAS, the multiplication would be carried out before the addition. This is not what is wanted
The question would want 3 times the SUM of 5 and 7.
To make sure you get the correct answer, you would have to write the expression slightly different
The correct way would be:
3(5 + 7)
✽➶ Hope This Helps You!
➶ Good Luck (:
➶ Have A Great Day ^-^
↬ ʜᴀɴɴᴀʜ ♡
The first three steps of completing the square to solve the quadratic equation x2 +4x -6 0, are shown below. Step 1: x2 +4x 6 Step 2: x2 +4x +4 6+4 Step 3: (x +2)2 10 What are the next 3 steps?
Answer:
step 4: Take the square root on both sides
√(x + 2)^2 = √10
step 5: Simplify
x + 2 = ±√10
Step 6: Solve for x
x = √10 - 2 and x = -√10 + 2
Step-by-step explanation:
Step 1: x^2 +4x = 6
Step 2: x^2 +4x +4 = 6+4
Step 3: (x +2)^2 = 10
The next 3 steps are:
step 4: Take the square root on both sides
√(x + 2)^2 = √10
step 5: Simplify
x + 2 = ±√10
Step 6: Solve for x
x = √10 - 2 and x = -√10 + 2
Hope this will helpful.
Thank you.
The solution of the given quadratic equation is,
x = 1.16 or -2+12i
The given expression is
x² +4x - 6 = 0,
Since we know that,
The definition of a quadratic as a second-degree polynomial equation demands that at least one squared term must be included. It also goes by the name quadratic equations. The quadratic equation has the following generic form:
ax² + bx + c = 0
Then, after comparison,
a = 1, b = 4 and c = -6
Therefore the given equation is an quadratic equation,
We can write it apply quadrature formula:
x = (-b ± √(b²-4ac))/2a
= (-4 ± √(16+24))/2
= 1.16 or -2+12i
Hence,
x = 1.16 or -2+12i
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which value of x is in the solution set of the following inequality -3×+5>17
Answer:
x < -4
Step-by-step explanation:
To solve the inequality, use inverse operations.
-3x + 5 > 17
-3x > 17 - 5 Subtract 5 from both sides.
-3x > 12 Divide both sides by -3.
x < -4 Flip the inequality sign since you divided by a negative.
Moving at its top speed a sloth would take 20 hours to go 3 miles on land. What’s that in miles per hour
Answer:
.15 mph
Step-by-step explanation:
3 miles/ 20 hours or 3/20
Answer:
6 hours and 42 minutes (402 minutes)
Step-by-step explanation:
20 ÷ 3 = 6.7 hours
6.7 hours = 6 hours and 42 mins
To check if our answer is correct:
Do the inverse
6. 7 hours x 3 = 20.1
Round it to nearest whole number, 20
Gym a charges a registration fee of 75 plus 35.65 per month for members. Gym B charges a registration fee of 164 plus 17.95 for members. After how many months would the total cost at gym a and gym b to be the same for members?
A.10 months
B.5 months
C.7 months
D. They will never be the same
Answer:
B: after 5 months
Step-by-step explanation:
Make to equations from the given information
Let y be the cost, and let x be the number of months
Gym 1: y = 35.65x + 75
Gym 2: y = 17.95x + 164
It wants to know when the cost will be the same, so set the 2 equations equal to each other and solve..
35.65x + 75 = 17.95x + 164
17.70x = 89 (subtract 17.95x and 75 from both sides)
x = 5.02 (divide both sides by 17.7)
So after 5.02 months the cost will be equal, since 5.02 is greater than 5 months, the answer is after 5 months, which is B
The square pyramid has a base area of 900 square meters and a height of 40 meters. Find the volume.
Answer:
12000 m³
Step-by-step explanation:
The volume (V) of a pyramid is calculated using the formula
V = [tex]\frac{1}{3}[/tex] × area of base × height, hence
V = [tex]\frac{1}{3}[/tex] × 900 × 40 = 300 × 40 = 12000 m³
Answer:
12000 no problem
Step-by-step explanation:
I would like to know the result of 3^3
Answer:
[tex]3^{3}[/tex] = 27.
Step-by-step explanation:
3 to the third power ( [tex]3^{3}[/tex] ) is the same as :
3 x 3 x 3 which would equal :
3 x 3 = 9 x 3 = 27.
Hope this helps,
Davinia.
27
3 times.3 times 3
9 times 3
27
find the area of a rectangle whose length is 5 centimeters and width is 3 centimeters
your answer is 15 centimeters
If K is the midpoint of JL, JK= 8x + 11 and KL = 14x-1, find JL
JK=KL
Substitute
8x+11= 14x-1
-8x -8x
----------------------
11 = 6x-1
+1 +1
-----------------------
(÷6)12=6x (÷6)
------------------------
x = 2
JK+KL= JL
Substitute
8x+11+14x-1
8(2) +11+14(2)-1
---------------------------
16+10+ 28
26+28
54
JL=54
1). Linear Combination (SHOW WORK)
3x +2y = −4
4x − y= 13
2). graph
y= 1/2 x + 3
-3x+y=-2
Answer:
Part 1) The solution of the system of equations is (2,-5)
Part 2) The solution of the system of equations is (2,4)
Step-by-step explanation:
Part 1) Linear combination
we have
[tex]3x+2y=-4[/tex] -----> equation A
[tex]4x-y=13[/tex] -----> equation B
Multiply equation B by 2 both sides
[tex]2(4x-y)=2*13[/tex]
[tex]8x-2y=26[/tex] -----> equation C
Adds equation A and equation C
[tex]3x+2y=-4\\8x-2y=26\\-------\\3x+8x=-4+26\\11x=22\\x=2[/tex]
Find the value of y
[tex]3(2)+2y=-4[/tex]
[tex]2y=-4-6[/tex]
[tex]2y=-10[/tex]
[tex]y=-5[/tex]
The solution of the system of equations is (2,-5)
Part 2) By graph
[tex]y=(1/2)x+3[/tex] -----> equation A
[tex]-3x+y=-2[/tex] -----> equation B
we know that
The solution of the system of equations is the intersection point both graphs
Using a graphing tool
The intersection point is (2,4)
therefore
The solution of the system of equations is the point (2,4)
see the attached figure
Find an equation of the line passing through the pair of points. Write the equation in the form Ax+By=C
(-7,2), (-8,-9)
Answer:
11x - y = -79Step-by-step explanation:
The standard form of an equation of a line:
[tex]Ax+By=C[/tex]
The point-slope form of an equation of a line:
[tex]y-y_1=m(x-x_1)[/tex]
m - slope
(x₁, y₁) - point
We have the points (-7, 2) and (-8, -9). Substitute:
[tex]m=\dfrac{-9-2}{-8-(-7)}=\dfrac{-11}{-1}=11[/tex]
[tex]y-2=11(x-(-7))\\\\y-2=11(x+7)[/tex]
Convert to the standard form:
[tex]y-2=11(x+7)[/tex] use the distributive property a(b + c) = ab + ac
[tex]y-2=11x+77[/tex] add 2 to both sides
[tex]y=11x+79[/tex] subtract 11x from both sides
[tex]-11x+y=79[/tex] change the signs
[tex]11x-y=-79[/tex]
Santos wants to know what percentage of people who get married in his county knew each other in school. Which of the following survey methods will allow Santos to make a valid conclusion about the percentage of couples married in his county who knew each other in school?
Answer: Sort a list of couples married in his county into a random order, then ask the first 30 couples on the list.
Step-by-step explanation:
Answer:
b. Sort a list of couples married in his county into a random order, then ask the first 30 couples on the list.
Step-by-step explanation:
please mark me brainlist
im not just going to leave you guys with this explaination because i dont really like people just putting answers up when it's wrong just for the points thats why i try to show proff on MOST of my work
the screenshot is below
What is the factored form of x2 - 12x - 45?
Answer:
(x - 15)(x + 3)
Step-by-step explanation:
Factors of 45 include 5 and 9, 3 and 15, 1 and 45, and so on.
Note that 3*15 =+45; this is not what we wanted. Thus, try (-3)*15 = -45.
Do -3 and 15 combine to yield -12? No. Thus drop (-3)(15) and try (3)(-15).
Do 3 and -15 combine to yield -12? YES
Therefore, the factored form of x² - 12x - 45 is (x - 15)(x + 3).
Multiple choice math
4) - 4w^3
3rd answer
5)4th answer
6)4th answer
Answer:
4) - 4w^3
3rd answer
5)4th answer
6)4th answer
Step-by-step explanation:
I had the same thing
Solve for x. 3x+1=7 What is the root? If there is no root, choose none.
12
16
16 2/3
none
I think the root of "3x + 1 = 7" is 2...
Answer:
The root of the equation is x=2.
Step-by-step explanation:
Given : Equation [tex]3x+1=7[/tex]
To find : Solve for x?
Solution :
Step 1 - Write the equation
[tex]3x+1=7[/tex]
Step 2 - Subtract 1 both side,
[tex]3x+1-1=7-1[/tex]
[tex]3x=6[/tex]
Step 3 - Divide the equation by 3,
[tex]\frac{3x}{3}=\frac{6}{3}[/tex]
[tex]x=2[/tex]
Therefore, The root of the equation is x=2.
Which is the value of y in the following system? y=3x-5 6x+3y=15
Answer:
The value of y in the solution of the system is [tex]y=1[/tex]
Step-by-step explanation:
we have
[tex]y=3x-5[/tex] -----> equation A
[tex]6x+3y=15[/tex] -----> equation B
substitute equation A in equation B
[tex]6x+3(3x-5)=15[/tex]
[tex]6x+9x-15=15[/tex]
[tex]15x=15+15[/tex]
[tex]15x=30[/tex]
[tex]x=2[/tex]
Find the value of y
[tex]y=3(2)-5=1[/tex]
What is 6 1/3 - 1 2/3 ?
4/3 or it can be turned into a repeating decimal 1.333333....
Answer:
4 2/3
Step-by-step explanation:
First borrow the 6 for the 1/3. Now, it becomes 4/3. Then subtract. (6 4/3 - 1 2/3) which is 4 2/3.
A jar contains 2 sugar cookies, 5 peanut butter cookies, and 3 chocolate chip cookies.What is the probability of randomly choosing a sugar cookie, not replacing it, and then choosing a peanut butter cookie?
You would have 2/10 chance of choosing the sugar cookie then after you chosen it 5/9 chance of picking up a peanut butter cookie. I hope this helps
Answer:
1/9
Step-by-step explanation:
The total number of cookies is
2 sugar cookies+ 5 peanut butter cookies+ 3 chocolate chip cookies= 10
We want to take a sugar cookie
P(sugar cookie) = # sugar cookie/total cookies
= 2/10 = 1/5
Now we eat the cookie (not replacing it) so there are only 9 cookies
1 sugar cookies+ 5 peanut butter cookies+ 3 chocolate chip cookies= 9
Now we want a peanut butter cookie
P(peanut butter cookie) = # peanut butter cookie/total cookies
= 5/9
To get the probability of both events happening, multiply them together
P( sugar, peanut) = 1/5 * 5/9
= 1/9
Factor & Finding Zeros
x^{2} +12x+35=0
Answer:
x = - 7, x = - 5
Step-by-step explanation:
To factorise the quadratic
Consider the factors of the constant term (+ 35) which sum to give the coefficient of the x- term (+ 12)
The factors are + 7 and + 5, since
7 × 5 = 35 and 7 + 5 = 12, hence
x² + 12x + 35 = 0 ← in standard form
(x + 7)(x + 5) = 0 ← in factored form
Equate each factor to zero and solve for x
x + 7 = 0 ⇒ x = - 7
x + 5 = 0 ⇒ x = - 5