Answer:
Applying the quadratic formula.
Exact Form:
x=32,−92
Decimal Form:
x=1.5,−4.5
Mixed Number Form:
x=112,−412
Step-by-step explanation:
Solve the equation: x2 + 3x -27/4 = 0 With the coefficients: a = 1, b = 3, c = -6.75 a ≠ 0 With ∆ = 36> 0 => Equation has 2 distinct solutions
x1 = 1.5, x2 = -4.5
4.1 Warm-Up
Tuesday
Video Example:
Write the algebraic rule that represents the dilation that was applied.
You Try:
Which rule best represents the dilation that has been applied?
(x, y) → (2x, y)
(x, y) → (0.5x, 0.5y)
(x, y) → (2x, 2y)
(x, y) → (2 + x,2 + y)
Wednesday
Video Example:
Triangle XYZ is dilated with the origin as the center of dilation using the rule (x, y)(0.5x, 0.5y) to create Triangle X’Y’Z’. Which statement is true?
Triangle A’B’C’ is larger than Triangle ABC, because the scale factor is greater than 1
Triangle A’B’C’ is smaller than Triangle ABC, because the scale factor is less than 1
Triangle A’B’C’ is smaller than Triangle ABC, because the scale factor is greater than 1
You Try:
A figure will be dilated on a coordinate grid to create a smaller figure. The figure is dilated using the origin as the center of dilation. Which rule could represent this dilation?
(x, y) (0.5 + x, 0.5+y)
(x, y) (0.5 - x, 0.5-y)
(x, y) (32x, 32y)
(x, y) (23x, 23y)
Answer:
The answer is below
Step-by-step explanation:
The question is not complete but i would show how to solve.
Transformation is the movement of a point from its initial location to a new location. Types of transformation are dilation, rotation, translation and reflection.
Dilation is the enlargement or reduction in the size of a figure.
a) If an point A(x, y) is dilated by a factor k, the new coordinate is A'(kx, ky). From the above options the ones that represent dilation is (x, y) → (0.5x, 0.5y) and (x, y) → (2x, 2y) . If the object is reduced then the correct option is (x, y) → (0.5x, 0.5y) while if the object is enlarged the correct option is (x, y) → (0.5x, 0.5y)
b)Dilation is the enlargement or reduction in the size of a figure by a factor k. If k < 1, then it is a reduction and if k > 1, it is an enlargement.
Since Triangle XYZ is dilated with the origin as the center of dilation using the rule (x, y)⇒(0.5x, 0.5y) to create Triangle X’Y’Z’, since the factor is less than 1(0.5 < 1), it is a reduction. Hence Triangle X’Y’Z’ is smaller than Triangle XYZ, because the scale factor is less than 1
c) The dilation creates a smaller figure hence the factor of dilation should be less than 1.
Use the graph to answer the question.
y
5
4
3
2+
1
-4 -3 - -
3
4
5
X
N
1
-24
-3
-4+
-5
Which line is perpendicular to the line shown on the graph?
O A. y=-x+2
O y
B. y=-{x-4
oc. y = {x+1
OD. y = kx + 1
Answer:
C
Step-by-step explanation:
32/a = 12.8/5.6
Pls show work for brainest
(Question worth 12 points)
Answer:
a=14
Step-by-step explanation:
32/a=12.8/5.6
a(32/a)=(12.8/5.6)a
32=12.8/5.6a
5.6a(32)=(12.8/5.6a)5.6a
12.8a=179.2 or a = 179.2/12.8
a=14
Help (what is the correct answer)?
Answer:
C
Step-by-step explanation:
1) Convert 1/3 to a decimal
using long division
A company has 2.4 times 10 to the 6th power shares of stock and 1.5 times the 10 to the 4th power shareholders. If each shareholder owned the same number of shares, how many shares would each shareholder own? Write your answer in scientific notation
Answer: 1.6 * 10² shares
Step-by-step explanation:
Number of shares company has = 2.4 * 10⁶
Number of shareholders = 1.5 * 10⁴
Number of shares each shareholder owns:
= 2.4 * 10⁶/1.5 * 10⁴
= 2.4/1.5 * 10⁶⁻⁴
= 1.6 * 10²
A large soup pot holds 20 quarts of soup. What could be its volume in liters? (Note a
liter is slightly larger than a quart)
a. 7.57
b. 19
c. 21
d. 75.7
Answer:
a
because it is math
simple math
VERY simple math
-2x - 14 =-2
(Solve for x)
Answer:
x = -6
Step-by-step explanation:
Answer:
x=-6
Step-by-step explanation:
-2x - 14 = -2
first, you have to add 14 to both sides
-2x = 12
now you divide -2 from both sides
x = -6
Bodie purchases a rectangular prism ( a box ) to store his dog food in. The prism is LaTeX: \frac{7}{4}7 4 inches long, LaTeX: \frac{9}{4}9 4 inches wide, and 3 inches in height. Bodie's dog food are these cute little cubes that are each LaTeX: \frac{1}{4}1 4 inches long, wide, and high. If Bodie carefully stacks the dog food into the prism, how many little dog food cubes will fit in the prism?
Answer:
84dog cubes
Step-by-step explanation:
First we need to get the volume of the rectangular prism and the little cubes
Volume of the prism = base area × height
Volume f the prism = length × width × height
Given
Length = 7/4in
Width = 9/4in
Height = 3in
Volume of the prism = 7/4×9/4×3
Volume of the prism = 63/48
Volume of the prism= 21/16 in³
Volume of the cube = L³
L is the length of one side of the cube
Volume of the cube =(1/4)³
Volume of tje cube = 1/64in³
Number of dog food cubes that will fit in = 21/16÷1/64
= 21/16×64/1
= 21×4
= 84
Hence 84 dog cubes will fit in
If MNP - TSR and NQ and SU are angle bisectors, find TS.
MN = 2
TS = n + 2
NP = 3
SU = 1
NQ = n + 3
Answer:
TS is 1
Step-by-step explanation:
The given parameters are;
ΔMNP is similar to ΔTSR
[tex]\overline {NQ}[/tex] and [tex]\overline {SU}[/tex] are angle bisectors of ∠MNP and ∠TSR respectively
MN = 2, TS = n + 2, NP = 3, SU = 1, NQ = n + 3
We have;
MN and TS are corresponding sides
[tex]\overline {NQ}[/tex] and [tex]\overline {SU}[/tex] are corresponding sides
Therefore, we have;
MN/TS = [tex]\overline {NQ}[/tex]/[tex]\overline {SU}[/tex] which gives;
2/(n + 2) = (n + 3)/1
(n + 2)·(n + 3) = 2
n² + 3·n + 2·n + 6 = 2
∴ n² + 5·n + 4 = 0, which gives, by factorization;
(n + 1)·(n + 4) = 0
∴ n - 1 or n = -4
TS = n + 2
When n = -1 TS = -1 + 2 = 1
When n = -4, TS = -4 + 1 = -3
Therefore, for a natural number value, we have, n = -1 and TS = 1.
Please Help Meh I dont Get this
For what value of x can the given lengths
be side lengths of a right triangle?
28, x, 53
Answer:
45
Step-by-step explanation:
The formula for finding the longest size of a right angle is
[tex]c^{2} = a^{2} + {b}^{2}[/tex]
a = 28, b = ? and c = 53;
Therefore, if you make b the subject of the formula, you will have
[tex]b = \sqrt{ {c}^{2} - {a}^{2} } [/tex]
And after plugging the value of c=53 and a=28, b is gotten to be 45
What is the value of -17 - (-1)?
Answer: it’s 1
Step-by-step explanation:
A negative num
Evaluate the expression for b=5.
4b2
Step-by-step explanation:
When b = 5,
4b² = 4(5)² = 4 * 5 * 5 = 100.
Answer:
100 is the right answer.
Step-by-step explanation:
Given that b=5
4b² = 4(5)² = 4×25 = 100
Y=-x^2-12x-37 find the 1) Roots 2) Factors 3) Vertex (x,y) 4) Interception with 'Y" axis 5) Axis of Symmetry 6)Direction of Opening 7)Max / Min ? Coordinates 8)Sketch 9) Domain 10) Range
Answer:
1) The roots of the equation Y = -x² - 12·x - 37 are x = -6 - √73 and -6 + √73
2) The factors of the function Y = -x² - 12·x - 37 are (x + (-6 - √73)) and (x - (-6 + √73))
3) The vertex is (-6, -1)
4) The Y-intercept is (0, -37)
5) The axis of symmetry is x = -6
6) The parabola opens downward
7) The maximum point is (-6, -1)
8) The graph of the function created with Microsoft Excel is attached
9) The domain of the function is -∞ < x < ∞
10) The range of the function is -∞ < Y ≤ -1
Step-by-step explanation:
The given function is Y = -x² - 12·x - 37
1) The roots of the equation Y = -x² - 12·x - 37 is given as follows;
0 = -x² - 12·x - 37
∴ -x² - 12·x - 37 = 0
The roots are;
x = (12 ± √((-12)² - 4 × 1 × (-37)))/(-2)
∴ x = -6 - √73 and -6 + √73
2) The factors are (x + (-6 - √73)) and (x - (-6 + √73))
3) The vertex is given by h = -b/(2·a) = 12/(2) = -6
k = c - b²/(4·a) = -37 - 144/(-4) = -1
The vertex = (h, k) = (-6, -1)
4) The intercept with the "Y" axis is given when x = 0, therefore, the y-intercept is (0, -37)
5) The axis of symmetry can be found at the vertex or the line x = -6
6) The sign of the coefficient of x² is negative therefore, the parabola opens downward
7) The maximum point is given as follows;
At the maximum point, dY/dx = d(-x² - 12·x - 37)/dx = -2·x - 12 = 0
x = 12/(-2) = -6, which is the vertex, therefore Y = -(-6)² - 12×(-6) - 37 = -1
The maximum point is the vertex (-6, -1)
8) Please find attached the graph of the function created with Microsoft Excel
9) The domain of the function is -∞ < x < ∞
10) The range of the function is -∞ < Y ≤ -1
What is 3f + 8f - 8f - 3f simplified?
Answer:
0
Step-by-step explanation:
everything cancels out so the answer is 0
Answer:
0
Step-by-step explanation:
3f + 8f - 8f - 3f
commutative property
(3f - 3f) + (8f - 8f)
3 - 3 = 0
0f + (8f - 8f)
8 - 8 = 0
0f + 0f
combine like terms
0 + 0 = 0
0f, or just 0
|3x-4| +2=1
Please help!
1.6 !!!!!!!!!! x=1.6 !!!!!
Jerry started sit-ups every day . The first day he did 15 sit up . Everyday he did 2 more sit ups than he did the previous day today jerry did 33 sit-ups
Answer:
2x+15=33
Step-by-step explanation:
Computation of the equation that could be solved to find the number of days Jerry has been doing sit-ups, not counting the first day
Based on the information given the EQUATION will be :
2x+15=33
Where,
x represent Jerry Sit up numbers of days excluding the first day
2x represent the additional 2 more sit ups
2x +15 represent the total number of sit up that was done after the first day
2x+15=33 represent the total 33 sit-ups that jerry did today
Therefore the EQUATION that could be solved to find the number of days Jerry has been doing sit-ups, not counting the first day will be 2x+15=33
What is the image of the point (-9, 1) after a rotation of 90° counterclockwise about
the origin?
Answer:
(- 1, - 9 )
Step-by-step explanation:
Under a counterclockwise rotation about the origin of 90°
a point (x, y ) → (- y, x ) , so
(- 9, 1 ) → (- 1, - 9 )
The image of the point (-9, 1) after a rotation of 90° counterclockwise about the origin is (1, 9).
What is rotation rule of 90°?Here are the rotation rules: 90° clockwise rotation: (x, y) becomes (y, -x) 90° counterclockwise rotation: (x, y) becomes (-y, x) 180° clockwise and counterclockwise rotation: (x, y) becomes (-x,-y).
The given coordinate point is (-9, 1).
Rule: (x, y)→(y, -x)
The image of the point (-9, 1) is
(-9, 1)→(1, 9)
Therefore, the image of the point (-9, 1) after a rotation of 90° counterclockwise about the origin is (1, 9).
Learn more about the rotation of 90° counterclockwise here:
brainly.com/question/1571997.
#SPJ2
goodmorning, can somebody help me plsss
Answer: I believe it's c. atoms form molecules
Step-by-step explanation:
because atoms are the smallest unit of matter and when atoms join together they form a larger unit of matter called molecules.
The difference between two numbers is 4. If the larger number is equal to wo more than three times the smaller number. What are the two numbers
Answer:
1 and 5
Step-by-step explanation:
s = smaller number
l = larger number = 2 + 3s
2 + 3s - 1s = 4
2 + 2s = 4
2s = 2
s = 1
l = 2 + 3(1)
l = 5
please solve this question in mathematics
75*75+4543-8745/3.5
Answer:
7669.42857
Step-by-step explanation:
Add parentheses to the following equation to make it true.
[tex]12*2-3+4*2=-4[/tex]
Answer:
[tex]12 * (2 - 3) + (4 * 2)[/tex]
Step-by-step explanation:
Follow PEMDAS for the given answer.
PEMDAS is the order of operation, and is:
Parenthesis
Exponents (& Roots)
Multiplication
Division
Addition
Subtraction.
Reverse solve the answer so that the result is the question.
First, solve the parenthesis:
12 * (2 - 3) + (4 * 2)
12 * (-1) + 8
Next, multiply 12 and -1 together:
12 * -1 = -12
Finally, add:
-12 + 8 = -4
12 * (2 - 3) + (4 * 2) is your answer.
~
[tex]12 \times (2 - 3) + (4 \times 2)[/tex]
Step-by-step explanation:
Add parentheses to the following equation to make it true.
[tex]12 \times 2 - 3 + 4 \times 2 = - 4[/tex]
________________[tex] = 12 \times 2 - 3 + 4 \times 2 = - 4[/tex]
[tex] = 12 \times (2 - 3) + (4 \times 2)[/tex]
[tex] = 12 \times ( - 1) + 8[/tex]
[tex] = - 12 + 8[/tex]
[tex] = - 4[/tex]
The regular price of an ice cream cone is $1.25 but on Monday it sells for $0.95. Karen and her friends bought 5 ice cream cones on Saturday, 3 on Sunday and 4 on Monday. Calculate the average price they paid for ice cream.
Answer:
$13.8
Step-by-step explanation:
I did the math
Isaiah measured a pencil to be 4.8 inches. The actual measurement is 4 inches. What is Isaiah's percent error?
Answer:
80%
Step-by-step explanation:
The actual value measurement = 4
Estimated value of the measurement= 4.8
percent error= (Estimated value - actual value) ×100%
= (4.8-4)×100%
=0.8×100%
=80%
Hence, Isaiah's percent error is 80%
Answer:
20%
Step-by-step explanation:
I did this on a test and I got it right trust me
3-7/8
please answer :p
Answer:
2.125 is your answer!! pls give brainlist (:
Step-by-step explanation:
10.25 divided by -0.5 =
Answer:
20.5 this is the answer 10.25 divided by 0.5
X<-5
Graphing the inequality
Answer:
Draw the graph of line x=5 , which would be vertical line passing through (5,0) . Since x is less than but not equal to 5 , make it a dotted line and shade the region to the left.
Step-by-step explanation:
6 - 2 4/7 = ?
answer asap and correct pls.
Answer:
24/7
Step-by-step explanation:
Please put them in order THANK YOU