Answer:
k=7
Other root=3
Step-by-step explanation:
If x=4 is a root of the given equation, then it satisfies the given equation.
4^2-k(4)+12=0
We can solve this equation for k.
16-4k+12=0
28-4k=0
28=4k
28/4=k
7=k
So the equation is x^2-7x+12=0
Factor form is (x-3)(x-4)=0 since-3(-4)=12 and -3+-4=-7.
This implies x=3 and x=4 are roots.
What is the value of the expression below when y = 5? Show your work and write your answer in a complete sentence.
Y exponent 2-3y+6
Answer:
y=1
Step-by-step explanation:
5=2-3y+6
3y=2-5+6
3y= -3+6
3y= 3
3y÷3=3÷3
y=1
Answer:
16
Step-by-step explanation:
Substitute y = 5 into the expression
y² - 3y + 6
= 5² - 3(5) + 6
= 25 - 15 + 6
= 16
Denise buys a tote bag at a gift shop for $12. The same bag is available at Denise's pharmacy for 2/3 the price she paid at the gift shop. Let's say you have enough money to buy 10 bags from the gift shop. How many bags can you buy from the pharmacy with the same amount of money? A.3 B.12 C.15 D.18
Answer:
15
Step-by-step explanation:
The price of the bag at the pharmacy is
2/3 * 12 = 8 dollars
You have enough for 10 at the gift shop
10 * 12 = 120
Take 120 dollars and divide by 8 dollars to see how many you can get at the pharmacy
120/8 =15
Answer:
the answer is C. it was on my mid-term
Step-by-step explanation:
Please help with this
Find the area of the shaded regions.
Answer:
The area of the shaded region is 7π square centimeters.
Step-by-step explanation:
Note that Circle B has a radius of 3 cm, and the two smaller circles, Circles O and C, both have a radius of 1 cm.
The area of a circle is given by:
[tex]\displaystyle A = \pi r^2[/tex]
Therefore, the area of Circle B, the entire circle, is:
[tex]\displaystyle \begin{aligned} A_B &= \pi (3)^2 \\ &= 9\pi \end{aligned}[/tex]
The area of Circle O is:
[tex]\displaystyle \begin{aligned} A_O &= \pi (1)^2 \\ &= \pi \end{aligned}[/tex]
And likewise, the area of Circle C is:
[tex]\displaystyle \begin{aligned} A_C &= \pi (1)^2 \\ &= \pi \end{aligned}[/tex]
The area of the shaded area is the area of the Circle B subtracted by the area of Circles O and C. Hence:
[tex]\displaystyle A_\text{shaded} =A_B - \left(A_ O + A_ C\right)[/tex]
Substitute and evaluate:
[tex]\displaystyle \begin{aligned} A_\text{shaded} &= (9\pi ) - (\pi + \pi) \\ &= 9\pi - 2\pi \\\ &= 7\pi \end{aligned}[/tex]
The area of the shaded region is 7π square centimeters.
Gabriel's family is investing $5,000 into two different bonds for college. One bond gave
an interest of 5% per year, and the other 3%. If the combined interest for the year was
$220, how much money was invested in each bond?
The amount invested in the bond that yields the 5% interest is $3500 while the amount invested in the bond that yields the 3% interest is $1500
In order to determine the amount invested in each bond, simultaneous equation would be used
From the question, two sets of equations can be derived
0.05x + 0.03y = 220 equation 1
x + y = 5000 equation 2
Where :
x = amount invested in the bond that gives 5% interest
y = amount invested in the bond that gives 3% interest
Multiply equation 2 by 0.03
0.03x + 0.03y = 150 equation 3
Subtract equation 1 from 3
0.02x = 70
Divide both sides of the equation by 0.02
x = 3500
Substitute for x in equation 2
3500 + y = 5000
Subtract y from both sides of the equation
y = 5000 - 3500
y = 1500
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i  genuinely dont know help
Answer:
-13 1/2 < -6/8
Step-by-step explanation:
*Any negative in either the numerator or denominator will make the entire fraction negative.
1/2 = .5
-13 1/2 = -13.5
-6/8 = -3/4
-3/4 = -0.75
-6/8 = -0.75
-13 1/2 = -13.5
Which means:
-13 1/2 < -6/8
Hope this helped.
Answer:
[tex] < [/tex]
Step-by-step explanation:
[tex] \frac{6}{8} [/tex]
Is close to 0 (to positive) you can use a time line to determine which is a correct answer
Determine if the expression -5y^5-y^3 is a polynomial or not. If it is a polynomial, state the type and degree of the polynomial.
Answer:
Yes, it is a polynomial, and the degree is 5
Step-by-step explanation:
A polynomial is a combination of terms separated using + or − signs and normally have exponents. So, this equation is a polynomial. The degree is just the highest exponential value, which is 5 because -5y is being raised to the 5th power
calculate using the distributive property
7×19
Answer:
133
Step-by-step explanation:
7 * 19
Rewrite 19 as 20 -1
7 * (20-1)
Distribute
7*20 - 7*1
140 - 7
133
Can you please help me!!!!!
The cross-section of a searchlight mirror is shaped like a parabola. The light bulb is located 3 centimeters from the base along the axis of symmetry. If the mirror is 20 centimeters across at the opening, find its depth in centimeters. (Round your answer to the nearest tenth if necessary.)
The depth of the mirror of the cross-section of a searchlight would be 8.33 cm if the light bub has a vertex at 3 cm and the mirror is 20 centimeters across at the origin.
A cross-section is perpendicular to the axis of the symmetry goes through the vertex of the parabola. The cross-sectional shape of the mirrored section of most searchlights or spotlights is parabolic.
It helps in maximizing the output of light in one direction.The equation of the cross-section of the parabola is - [tex]y^{2} = 4ax[/tex], where a is the focus and x is the depth of the mirror from its origin.Given:
a = 3
y = [tex]\frac{20}{2}[/tex] cm = 10 cm
Solution:
from the equation [tex]y^{2} = 4ax[/tex]
[tex]y^{2} = 4*3*x\\ y^{2} = 12x[/tex]
putting x, 10 cm in the equation
[tex]x=\frac{10^{2} }{12} \\\\x= \frac{100}{12} \\\\x= 8.33 cm[/tex]
thus, the depth of the mirror would be - 8.33 cm
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HELLLPPPPPPPPP!!!!!!
a cake recipe calls for 4 1/2 cups of sugar. a caterer has 50 1/2 cups of sugar on hand. how many cakes can he make?
Answer:
11 cakes. he can make 11 cakes
Answer:
11
Step-by-step explanation:
You have to do 4 x the amount you know you can such as 10.
Then you have to multiply the 1/2 by that same number
So we'd get 4x10=40 and 1/2x10=5 to get 45
Then we add 45+4 1/2 = 49 1/2
They can make 11 cakes
Tricia starts school at 7:00 AM and has lunch at 12:00 PM. She wants to make sure she has something to eat in between. Determine what time she should eat her snack if she is to eat at exactly a time between starting school and eating lunch. (Hint: Set up a horizontal number line as a timeline.) A. A. 9:30 AM
B. 10:00 AM
C. 9:00 AM
D. 10:30 AM
Answer:
D) 9:00 am
Step-by-step explanation:
Because 9:00 is the midpoint of 7 and 12
On two investments totaling $9,500, Peter lost 3% on one and earned 7% on the other. If his net annual receipts were $169, how much was each investment?
Answer:
23$ was each investment
Step-by-step explanation:
[tex]\sqrt{x} x^{2}[/tex] +3
solve for the measure of c pt 2 (18pts)
Answer:
d: 20
Step-by-step explanation:
alternative angle
arrange in order smallest to largest 0.38, 0.31 , 0.4
Answer:
0.4 , 0.31 , 0.38 is the answer
√2+1
b) Rationalize the denominator:
√2+1
Answer:
there is not a complete question here ...
[tex]\sqrt{2} +1[/tex] is not in a denominator to rationalize
if it were you would multiply the rational expression (the fraction)
by [tex]\frac{\sqrt{2} -1}{\sqrt{2} -1}[/tex] the result (in the denominator would end up being "2 -1"
which is 1
Step-by-step explanation:
Solve x^3 = 64/27
Picture has answer choices
Answer:
x = 4/3
Step-by-step explanation:
x^3 = 64/27
Take the cube root of each side
(x^3)^1/3 =( 64/27)^1/3
x = 4/3
Answer:
4th option
Step-by-step explanation:
Given
x³ = [tex]\frac{64}{27}[/tex] ( take the cube root of both sides )
[tex]\sqrt[3]{x^3}[/tex] = [tex]\sqrt[3]{\frac{64}{27} }[/tex]
x = [tex]\frac{\sqrt[3]{64} }{\sqrt[3]{27} }[/tex] = [tex]\frac{4}{3}[/tex]
can uh help me in this
Answer:
Step-by-step explanation:
b) a² - 1 + b(b - 2a) = a² -1 + b*b - b*2a {distributive property}
=a² - 1 + b² - 2ab
= (a² - 2ab + b² ) - 1
= (a - b)² - 1² {use identity x²-y²= (x+ y)(x -y)}
= (a - b + 1)(a -b +1)
b) 15 +8y + y² - 2x - x² = (y² + 8y + 15) - x² - 2x
= (y² + 5y + 3y + 15) - x(x + 2)
= [ y(y + 5) + 3(y +5)] - x(x + 2)
= [(y + 5)(y+3) ] - x(x +2)
Solve for b.
106 + 18 = 28
Answer:
106+18≠28
106+18=124
in case the b was misplaced with the 6
10b=28-18
10b=10
10b/10=10/10
b=1
hope this is helpful
Which of the following equations has exactly one solution?
A. 4x – 4 + 2x = 6x - 4
B. 2(4x + 5) = 8x + 10
C. 4x - 8 = 4(x - 4)
D. 3x + 5 = 2x - 6
The equation with exactly one solution is 3x + 5 = 2x - 6. Option D is correct.
To determine which equation has exactly one solution, we need to solve each equation and see if we end up with a unique value for 'x'.
4x – 4 + 2x = 6x - 4
Combine the x terms on the left side: 6x - 4 = 6x - 4
This equation is an identity and holds true for all values of x. It doesn't have a unique solution.
B. 2(4x + 5) = 8x + 10
Distribute the 2 on the left side: 8x + 10 = 8x + 10
Similar to the previous equation, this equation is also an identity and holds true for all values of x.
It doesn't have a unique solution.
4x - 8 = 4(x - 4)
Distribute the 4 on the right side: 4x - 8 = 4x - 16
Subtract 4x from both sides: -8 = -16
This equation is contradictory and has no solution.
3x + 5 = 2x - 6
Subtract 2x from both sides: x + 5 = -6
Subtract 5 from both sides: x = -11
This equation has a unique solution, x = -11.
So, the equation with exactly one solution is 3x + 5 = 2x - 6. Option D is correct.
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I'm Timed
Which situation could this expression represent?
6 + 15 ÷ 3
Michael has 6 stamps in his collection. He adds 15 more stamps to the collection. He divides the collection into 3 piles. How many stamps are in each pile?
Walter has 6 stamps in his collection. He divides the stamps evenly into 3 piles and adds 15 new stamps to one of the piles. How many stamps are in this pile?
Andy has 15 stamps in his collection. He divides the stamps evenly into 3 piles and adds 6 stamps to one of the piles. How many stamps are in this pile?
Brycen has 15 stamps in his collection. He adds 6 more stamps to the collection. He divides the collection into 3 piles. How many stamps are in each pile?
Answer:
It's Micheal because he started with 6 and added 15 and he divided them into 3 piles
What is the area of the polygon below
Which is the mode for the data set? −1, 0, 3, 4, −3, −1
0.3 −1 2 −0.5
Answer:
-1
Step-by-step explanation:
Mode is the number that appears most often
−1, 0, 3, 4, −3, −1
-1 appears twice which is more than any other number
-1 is the mode
The square pyramid pictured below has a surface area of
9 m
6 m
6 m
What is the radius of a sphere with a surface area of 100πcm2?
Answer:
5cm
Step-by-step explanation:
A=4πr2 = 100πcm2
r = 5
Is 64 a rational number or irrational?
Answer:
Step-by-step explanation:
the answer is irrational hope this helps
Answer:
Rational.
Step-by-step explanation:
64 is a rational number because it's a whole number. Irrational numbers are real numbers including: [tex]\pi, \sqrt{2}[/tex], and etc. Basically, rational numbers are anything that can be expressed as the quotient of two integers: 64/1
what is the equation of the line that passes through the point (3,-7) and has a undefined slope
Answers:-
y = mx+b where m is the slope and b is the y intercept.
The line must pass through (3,-7) therefore
-7 =3 m +b
Now solve for b
b=-7 - 3m
Now substitute b into the definition of a line
y = mx -7 -3m
y=m*(x-3) -7
Now check the solution to see if for every m it passes through (3,-7)
substituting x in to the solution.
y=m(3–3)-7
y=7 hence the solution is correct. for any m
Plz follow ma );
Answer:
y = 7
Step-by-step explanation:
y = mx+b where m is the slope and b is the y intercept.
The line must pass through (3,-7) therefore ---> -7 =3 m +b
Now solve for b ---> b=-7 - 3m
Now substitute b into the definition of a line, y = mx -7 -3m ---> y=m*(x-3) -7
Now check the solution to see if for every m it passes through (3,-7)
Substitute x in to the solution ---> y=m(3–3)-7
y=7 therefore the solution is correct.
Which correlation best describes the data below.
Answer:
weak positive
Step-by-step explanation:
weak because the line of best fit (the line passes through all points and used to express the relationship between them) doesn't pass through all ponts here.
positive because the values of data points are rising throughout the graph.
Find the values of the unknown angles marked with letters. 50 points!!!!!!!
a ?
b ?
c ?
d ?
Answer:
a = 115°, alternate interior angles are congruentb = 70°, same as abovec = 180° - 115° = 65°, angles forming a straight angle are supplementaryd = 180° - 70° = 110°, same as aboveC:-
[tex]\\ \sf\longmapsto c+115=180[/tex]
[tex]\\ \sf\longmapsto c=180-115[/tex]
[tex]\\ \sf\longmapsto c=65°[/tex]
D:-
[tex]\\ \sf\longmapsto d+70=180[/tex]
[tex]\\ \sf\longmapsto d=180-70[/tex]
[tex]\\ \sf\longmapsto d=110°[/tex]
maths work summer vacations homework
Answer:
Step-by-step explanation:
line is made up of points and its endless
eg:........................................................................................it goes on forever even though it stopped here
a line segment is not endless it starts a one point and stops at another
eg: :-----------------------: see it stops its like starting a sentence and finshing it .
a ray is diffrent . i dont know how to explain so heres a pic
those orange things are called rays.
