Answer:
x=20 and x=-50
Step-by-step explanation:
To find the roots, we need to simply solve for x. We do this by first moving all of the terms to the left and setting the right side equal to 0.
-1000
x^2+30x-1000=0
Now, factor it.
What adds up to 30 but multiplies to get -1000?
-10 and 40? No, because they multiply to get -400.
-20 and 50? Yes, because they add up to 30 and multiply to get -1000.
(x-20)(x+50)
x-20=0
x=20
x+50=0
x=-50
So, the roots are x=20 and x=-50
Given :-
x² + 30x = 1000 .To Find :-
The roots of the equation .Solution :-
As we know that if the quadratic equation is in standard form which is ,
[tex] ax^2+bx + c =0[/tex]
Then its roots are given by ,
[tex] x =\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
So on converting the equation in standard form ,
[tex] x^2+30x -1000=0[/tex]
With respect to the standard form ,
a = 1b = 30c = -1000Substitute in the Quadratic formula ,
[tex] x =\dfrac{-30\pm \sqrt{(30)^2-4(1)(-1000)}}{2(1)}[/tex]
Simplify,
[tex] x =\dfrac{-30\pm\sqrt{900+4000}}{2}[/tex]
Add the numbers inside square root ,
[tex] x =\dfrac{-30\pm\sqrt{4900}}{2}[/tex]
Divide each term in numerator by 2,
[tex] x =\dfrac{-30}{2}\pm\dfrac{\sqrt{70^2}}{2}[/tex]
Simplify ,
[tex] x = -15 \pm 35 [/tex]
Separate the two solutions ,
[tex] x = -15 + 35 , -15 -35[/tex]
Simplify ,
[tex]x = 20 , -50 [/tex]
Hence the solution of the equation are 20 and -50 .
I hope this helps.
The value of y is
one-fourth
the value of x. Why is it addiction
Answer:
Ummm because its not a negative sign in front of it
Step-by-step explanation:
i d k t b h
please help me understand why these two questions use different methods for solving
and how to use each way correctly
Answer:
36
Step-by-step explanation:
the total sugar bags to be distributed= x=48
the total rice bags to be distributed= y=72
each family can take a package containing= 1x +2y
as each family can have 2 rice bags thus we can estimate the total number of families that can benefit by diving total no of rice bags by 2 which will be = 72/2 =36
the rice can be divided into 36 families
while the sugar bags can be divided into 48 families
as these have to be divided into packages so there will be 36 packages
that can be distributed into 36 families.
What rigid motion maps the one figure onto the other figure?
Answer:
a reflection
Step-by-step explanation:
imagine this is on a piece of paper, fold the paper in half "hotdog style" then they will be mapped on top of each other.
Which expression shows
another way to write (4^3)^3?
high points pls help
kayla wants to find the width, AB, of a river. she walks along the edge of the river 150 ft and marks point c. then she walks 32 ft further and marks point D. she turns 90° and walks until her location, point A, and point C are collinear. she marks point E at this location, as show.
Answer:
32 x 150 = A = 2 x 2 = c + b = 254
Step-by-step explanation:
Consider the equation
2/3(12 – Ax) – 4 = 9(6 x + B).
What values for A and B will result in an equation that has infinite solutions?
Answer:
A = -81
B = 4/9
Step-by-step explanation:
An equation that has infinite solutions suggests that the left side equals the right side.
Expand brackets:
[tex]\dfrac23(12-Ax)-4 = 9(6 x + B)[/tex]
[tex]\implies 4-\dfrac23Ax = 54x+9B[/tex]
Equate coefficients of x:
[tex]\implies -\dfrac23A=54[/tex]
[tex]\implies A=-81[/tex]
Equate constants:
[tex]\implies 4=9B[/tex]
[tex]\implies B=\dfrac49[/tex]
Help me with this please
Answer:
x = 2 and y = 3
Step-by-step explanation:
To find the x- intercept, let y = 0 in the equation and solve for x
3x + 2(0) = 6
3x + 0 = 6
3x = 6 ( divide both sides by 3 )
x = 2 ← x- intercept
To find the y- intercept, let x = 0 in the equation and solve for y
3(0) + 2y = 6
0 + 2y = 6
2y = 6 ( divide both sides by 2 )
y = 3 ← y- intercept
can someone help me with this please
Answer:
A.1: ∠BAC ≅ ∠BDC ≅ ∠EDF, ∠ACD ≅ ∠ABD ≅ ∠BDE ≅ ∠CDF
A.2: ∠1 ≅ ∠4, ∠2 ≅ ∠3 ≅ ∠5 ≅ ∠6
A.3: ∠2 ≅ ∠3
B.1: ∠ACD ≅ ∠CAB, ∠CDA ≅ ∠ABC, ∠DAC ≅ ∠BCA
B.2: ∠1 ≅ ∠3 ≅ ∠5, ∠2 ≅ ∠4 ≅ ∠6
see "additional comment" regarding listing pairs
Step-by-step explanation:
There are a number of ways angles can be identified as congruent. In each case, the converse of the proposition is also true.
opposite angles of a parallelogram are congruentcorresponding angles where a transversal crosses parallel lines are congruentalternate interior angles where a transversal crosses parallel lines are congruentvertical angles are congruentany two angles with the same measure are congruentIn these exercises, pairs of angles need to be examined to see which of these relations may apply.
__
ALeft
ABCD is a parallelogram, so the congruent angles are opposite angles and any that are vertical or corresponding:
∠BAC ≅ ∠BDC ≅ ∠EDF ≅ 110° (3 pairs)
∠ACD ≅ ∠ABD ≅ ∠BDE ≅ ∠CDF ≅ 70° (6 pairs)
Center
∠1 ≅ ∠4 ≅ 66° (1 pair) . . . . vertical angles
∠2 ≅ ∠3 ≅ ∠5 ≅ ∠6 ≅ 57° (6 pairs) . . . . marked with the same measure, and their vertical angles
Right
Assuming that lines appearing to go in the same direction actually do go in the same direction, the only pair of congruent angles in the figure is ...
∠2 ≅ ∠3
__
BLeft
Corresponding angles in congruent triangles are congruent. Here, the congruent triangles are ΔACD ≅ ΔCAB. So, the pairs of congruent angles are ...
∠ACD ≅ ∠CAB (30°)
∠CDA ≅ ∠ABC (90°)
∠DAC ≅ ∠BCA (60°)
Right
The corresponding angles and any vertical angles are congruent. This means all the odd-numbered angles in the figure are congruent, and all the even-numbered angles in the figure are congruent. The marked 72° angles show the "horizontal" segments are parallel by the converse of the corresponding angles theorem.
∠1 ≅ ∠3 ≅ ∠5 (72°) (3 pairs)
∠2 ≅ ∠4 ≅ ∠6 (108°) (3 pairs)
_____
Additional comment
The question asks you to list pairs of congruent angles. When 3 things are congruent, they can be arranged in 3 pairs:
a ≅ b ≅ c ⇒ (a≅b), (a≅c), (b≅c)
Similarly, when 4 things are congruent, they can be arranged in 6 pairs:
a ≅ b ≅ c ≅ d ⇒ (a≅b), (a≅c), (a≅d), (b≅c), (b≅d), (c≅d)
In the above, we have elected not to list all of the pairs, but to list the set of congruences from which pairs can be chosen.
Pleaseee help with this! Giving 60 points!
Answer:
X = 2, -8
Step-by-step explanation:
Answer:
A. ( x + 3 )² = 25
Step-by-step explanation:
2x² + 12x = 32
2(x² + 6x) = 32
x² + 6x + 9 = 16 + 9 [ addition of 9 from both sides ]
( x + 3 )² = 25
what is the perimeter of a circle
Please help me with this math problem!! Will give brainliest if correct! NO links please!
Answer:
x=31 <B=112
Step-by-step explanation:
I'm super lazy so I won't give a thorough explanation, but this should explain it all.
Opposite angles on parallelograms are congruent
I REALLY NEED HELP PLEASE!!
Answer:
4588 [in²].
Step-by-step explanation:
1) the given octagon can be imagined as 8 triangles (see the attachment). In order to calculate the required area of the octagon, it is enough to calculate the area of one triangle then increase it 8 times:
2) area of one triangle is:
37*31/2 [in²].
3) the required area of the octagon is:
31*37*8/2=31*37*4=4588 [in²].
A circle has an area of 2254 square inches. If the radius of the circle
is multiplied by 6, then what is the area of the new circle formed?
O A) 1000+ in.2
OB) 2270n in.
OC) 68057 in.2
OD 81007 in.2
Answer:
Answer: OD 81007 in.2
Step-by-step explanation:
Use formula for area of circle, which is A = πr²
The radius is squared, so if the radius or a new circle is 6 times larger (multiplied by 6), the difference in area will be 36 times greater. So the area is
225π(36) = 8,100π
Answer:
D) [tex]8100\pi[/tex] in²
Step-by-step explanation:
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Question:
A circle has an area of 225[tex]\pi[/tex] square inches. If the radius of the circle is multiplied by 6, then what is the area of the new circle?
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
area of a circle = [tex]\pi r^2[/tex] (where r is the radius)
⇒ [tex]\pi r^2=225\pi[/tex] in²
If the radius is multiplied by 6, then r = 6r
⇒ area = [tex]\pi (6r)^2=36\pi r^2[/tex]
Therefore, if [tex]\pi r^2=225\pi[/tex]
then [tex]36\pi r^2 = 36 \times 225\pi =8100\pi[/tex]
What is the graph of the system y = −2x 3 and 2x 4y = 8?.
Answer: C line through point (0,
3) and (1, 1). Line through (0, 2) and (4, 0)
Step-by-step explanation:
6. Shana wants to buy her dad a shirt that costs $46.20 for his birthday in 7 weeks. She wants to save the same amount of money each week. How much does she need to save each week? A $0.66 B $6.00 C $6.60 D $66.00
Answer: C $6.60
Step-by-step explanation:
46.20 ÷ 7 = 6.6
So Shana should be saving $6.60 every week.
helpp please 10 points ok
The correct answer is :
[tex]\frac{13}{50}[/tex]
Answer:
the fort effyh v answer is A duhhhhhh
2. Which of the following represents the value of an investment with a principal of $1500 with a nominal interest
rate of 2.5% compounded monthly after 5 years?
(1) $1,697.11
(3) $4,178.22
(2) $1,699.50
(4) $5,168.71
Answer:
(2) $1,699.50
Step-by-step explanation:
A(t) = P(1 + r/n)^nt
1500(1 + .025/12)^5*12
= $1699.50
$1,699.50 represents the value of an investment with a principal of $1500 with a nominal interest rate of 2.5% compounded monthly after 5 years.
What is compound interest?Compound interest is the interest on savings calculated on both the initial principal and the accumulated interest from previous periods.
Given that an investment with a principal of $1500 with a nominal interest rate of 2.5% compounded monthly after 5 years,
Amount = P(1+r/n)^nt
= 1500(1+0.25/12)^5*12
= $1699.50
Hence, $1,699.50 represents the value of an investment with a principal of $1500 with a nominal interest rate of 2.5% compounded monthly after 5 years.
For more references on Compound interest, click;
https://brainly.com/question/14295570
#SPJ2
(SHOW UR WORK) 98.73 ÷ 15 = ?
Answer:
3291÷500 or 6.582
Step-by-step explanation:
98.73 divide by 15 = 6.582
the question is confusing....
Answer:
[tex]c=35r+10[/tex]
Step-by-step explanation:
We need to create a linear equation in the form: c = mr + b
(where m is the slope and b is the y-intercept)
Choose two ordered pairs from the table: (2, 80) and (4, 150)
Let [tex](r_1,c_1)[/tex] = (2, 80)
Let [tex](r_2,c_2)[/tex] = (4, 150)
Calculate the rate of change (slope of linear equation) by dividing the change in c by the change in r:
[tex]\textsf{slope} \ m=\dfrac{c_2-c_1}{r_2-r_1}=\dfrac{150-80}{4-2}=35[/tex]
Now use point-slope form of linear equation to create final equation:
[tex]c-c_1=m(r-r_1)[/tex]
[tex]\implies c-80=35(r-2)[/tex]
[tex]\implies c=35r+10[/tex]
Susie is going on a run for 32 minutes she can run 1 mile in five minutes and she cools off for seven minutes how many miles can she run in her time limit
How do I find the value of x??
Add the two angles and then subtract from 180* to find the missing angle
So,
145* + 15* = 160*
180* - 160* = 20*
Answer: x = 20*
50 points!!! Please help ASAP!!!
Answer:
h (x)=-16x^(2)+3x+35 =
x-intercept(s): (3+√224932,0),(3−√2249 32,0)
y-intercept(s): (0,35)
find the equation of the line in point slope form of the line that passes through (-1, 4) and has slope 5
Answer:
y=5x+9
Step-by-step explanation:
5x because the slope is 5
then solve for b by plugging in x=-1, y= 4 into the equation y=5x+b
What is the value of the indicated angle
127
37
180
53
Answer:
53
Step-by-step explanation:
It is either an alternate angle or an opposite angle of the 53 shown.
We know that angles on a straight line add up to 180, so:
53+x=180
x=180-53
x=127
We know that the indicated angle plus x would give 180, so:
?+x=180
?+127=180
?=180-127
?=53
Cora is building towers of two different sizes using prism- and pyramid-shaped blocks. The diagram shows the ratio of prisms and pyramids in each tower. A tape diagram with 2 tapes of unequal lengths. The first tape has 4 equal parts. A curved bracket above the first tape is labeled Prisms. The second tape has 1 part of the same size as in the first tape. A curved bracket below the second tape is labeled Pyramids. A tape diagram with 2 tapes of unequal lengths. The first tape has 4 equal parts. A curved bracket above the first tape is labeled Prisms. The second tape has 1 part of the same size as in the first tape. A curved bracket below the second tape is labeled Pyramids. The table shows the number of prisms and the number of total blocks that Cora will use on each of her towers. Based on the ratio, complete the missing values in the table. Tower Prisms Total blocks AAA 161616 BBB 353535
Answer:
total blocks are 20 and prisms are 28
Step-by-step explanation:
There are 20 blocks needed for tower A, and 43.75 blocks needed for tower B
From the tape diagrams, we have the following ratio
Prism : Pyramid = 4 : 1
From the table, we have:
Tower A = 16 prisms
So, the ratio becomes
16 : Pyramid = 4 : 1
Multiply the ratio on the right-side by 4
16 : Pyramid = 16 : 4
By comparison, we have:
Pyramid = 4
This means that, 4 pyramid blocks are needed for tower A
So, the total number of blocks needed is:
Total = Pyramid + Prism
This gives
Total = 4 + 16
Evaluate the sum
Total = 20
Hence, there are 20 blocks needed for tower A
For table B, we have:
Tower A = 35 prisms
So, the ratio becomes
35 : Pyramid = 4 : 1
Express as fractions
[tex]\frac{Pyramid}{35} = \frac 14[/tex]
Multiply through by 35
Pyramid = 8.75
This means that, 8.75 pyramid blocks are needed for tower B
So, the total number of blocks needed is:
Total = 8.75 + 35
Evaluate the sum
Total = 43.75
Hence, there are 43.75 blocks needed for tower B
Read more about ratios at:
https://brainly.com/question/16981404
find the inverse of: 1:x --> 4-x/3 + 2
Answer:
[tex]f^{-1}(x)= \frac{3x}{2}+3[/tex]
Step-by-step explanation:
Interchange the variables:
x = y - 4 - [tex]\frac{y}{3} +2[/tex]
Solve for y:
[tex]y=\frac{3x}{2} +3[/tex]
Replace y with [tex]f^{-1} (x)[/tex] to show the final answer:
[tex]f^{-1}(x)= \frac{3x}{2}+3[/tex]
HELP PLS ‼️ A middle school student recorded 254 videos in 6 3/4 months. Find the student's video-taping rate in videos per month.
Answer:
127/4 or 31 3/4 or 31.75
Step-by-step explanation:
got this by dividing 254 with 6 3/4
Consider AABC with vertices A B C (3,1), (1, 2),and (4, 2) as shown in the accompanying diagram.
Is the triangle a right triangle? Justfify.
Answer:
yes; AB ⊥ BC
Step-by-step explanation:
If the triangle is to be a right triangle, the slopes of two sides must be opposite reciprocals. The slope is the ratio of rise to run.
mAB = rise/run = -3/4
mBC = rise/run = 4/3
These slopes, -3/4 and 4/3 are opposite reciprocals (their product is -1), so ...
AB ⊥ BC . . . the triangle is a right triangle
Creating production possibilities schedules and curves
Answer:
What is the question? You have put a statement or objective
in your own understanding, what does Principale of Contradiction mean?
Answer:
What is the meaning of principle of contradiction?
The principle of contradiction expresses the metaphysical and logical opposition between being and its negation. ... Formulated in the logical order, it asserts that it is impossible to affirm and at the same time deny the same predicate of the same subject.
Step-by-step explanation: