The solution of the given quadratic equation is x = (- 7 ± √(65)) / (2)
What is a quadratic equation?The meaning of quadratic equation is any equation containing one term in which the unknown is squared and no term in which it is raised to a higher power.
Given is a quadratic equation,
For this case, the first thing we must do is rewrite the polynomial:
x² + 7x - 4 = 0
We use the resolver to solve the problem using quadratic formula;
x = (- b ± √(b² - 4 × a × c)) / (2 × a)
Where,
a = 1
b = 7
c = -4
Substituting the values:
x = (- 7 ± √((7)² - 4 × (1) × (- 4))) / (2 × (1))
x = (- 7 ± √(49 + 16)) / (2×(1))
x = (- 7 ± √(65)) / (2)
Hence, The value of x is (- 7 ± √(65)) / (2)
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Question 1 of 20 Multiply. (4x - 5)^2
A. 16x2 - 25
B. 16x2 - 40x + 25
C. 16x2 + 20x + 25
D. 16x2 + 40x+ 25
Answer:
B) 16x² - 40x + 25
Step-by-step explanation:
1) Use square differences: (a - b)² = a² - 2ab + b².
[tex](4x)^{2} - 2 \times 4x \times 5 + {5}^{2} [/tex]
2)Use Multiplication Distributive Property: (xy)^a = x^a y^a.
[tex] {4}^{2} {x}^{2} - 2 \times 4x \times 5 + {5}^{2} [/tex]
3) Simplify 4² to 16.
[tex]16 {x}^{2} - 2 \times 4x \times 5 + {5}^{2} [/tex]
4) Simplify 5² to 25.
[tex]16 {x}^{2} - 2 \times 4x \times 5 + 25[/tex]
5) Simplify 2 × 4x × 5 to 40x.
[tex] {16x}^{2} - 40x + 25[/tex]
Thus, the Anwer is Option B) 16x² - 40x + 25 .
What's 8x3 please help me.
Answer:
24
Step-by-step explanation:
Answer: Equals 24! Have a great day!
Simplify the expression below.
4x+ 3(2x−1) − 4x
Answer:
=6x−3
Step-by-step explanation:
Let's simplify step-by-step
4x+3(2x−1)−4x
Distribute:
=4x+(3)(2x)+(3)(−1)+−4x
=4x+6x+−3+−4x
Combine Like Terms:
=4x+6x+−3+−4x
=(4x+6x+−4x)+(−3)
=6x+−3
Answer:
6x - 3
Step-by-step explanation:
4x + 3(2x - 1) - 4x
Distribute, multiply every term inside the parenthesis by the term outside of it,
4x + (3)(2x) + (3)(-1) - 4x
Simplify,
4x + 6x - 3 - 4x
Simplify further, combine like terms,
6x - 3
the composite figure is made up of three simpler shapes? what is the area of the figure
Answer:
B. 68 square cm
Step-by-step explanation:
0.5 x 6 x 5 = 15
5 x 7 = 35
9 x 2 = 18
15+35+18 =68
HELP HELP ASAP ASAP WILL MARK BRAINLIEST
ANSWER BOTH PLEASE EASY POINTS
Answer:
1.) Hypotenuse.
The hypotenuse is the longer side.
2.)Leg
Answer:
1.) Hypotenuse
2.) Leg
Step-by-step explanation:
The legs or bases of a triangle are the sides connected to the right angle.
The hypotenuse is the side across from the right angle and is always the longest side.
Solve 24=3r4. The solution is r=
what is the answer for this?
i tried 2 and it says wrong
Answer:
r=1.681793,−1.681793
Step-by-step explanation:
What is (-3, -2) reflected over the y-axis
Answer:
3,-2
Step-by-step explanation:
Answer:
(3, -2)
Step-by-step explanation:
[Cartesian plane]
______________
+y
↑
-x ← — | — → +x
(-3,-2) |
↓
-y
______________
[Flipping over the y axis]
-The reflection will be the-
same distance from the y axis
+y
↑
-x ← — | — → +x
(-3,-2) → | → (3, -2)
↓
-y
Help! With this math problem
Answer:
Its C
Step-by-step explanation:
up
Write an equation for the translation of x2 + y2 = 49 by 3 units left and 4 units
O(x + 3)2 + (y + 4)2 = 49
O(x + 3)2 + (y – 4)2 = 49
O(x – 3)2 + (y – 4)2 = 49
O(x – 3)2 + (y + 4)2 = 49
Answer: (x+3)^2+(y-4)^2=49
The answer is b :)
Step-by-step explanation:
Find the p and q that produce the Pythagorean triple (3, 4, and 5). Please help me, please and thank you! =)
Answer:
Step-by-step explanation:
Please help I would appreciate it
Answer:
Lower and upper quartiles(B)
Step-by-step explanation:
Form and solve an equation for .
2x
x+30
Answer:
x = 20
Step-by-step explanation:
The sum of the 3 angles in a triangle = 180°
Sum the angles in the triangle and equate to 180
2x + x + 30 + 90 = 180
3x + 120 = 180 ( subtract 120 from both sides )
3x = 60 ( divide both sides by 3 )
x = 20
Answer this plz I’m stuck on it
Answer:
The value of the car decreased by 16 percent.
Step-by-step explanation:
First I divided 15,540 by 18,500, and I got .84. Then, I subtracted .84 from 1, and got .16. Then I turned .16 into a percent, and got 16%.
Write the system of equations as a matrix equation AX=B, with A as the coefficient matrix of the system.
Please help!
Answer:
[tex]\left[\begin{array}{ccc}1&2\\6&7\end{array}\right]\cdot \left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}0\\-10\end{array}\right][/tex]
Step-by-step explanation:
The system of equation in matrix form is defined by following vector formula:
[tex]\vec A \cdot \vec x = \vec b[/tex] (1)
Where:
[tex]\vec A[/tex] - Matrix of coefficients.
[tex]\vec x[/tex] - Column vector of variables.
[tex]\vec b[/tex] - Column vector of results.
If we know that [tex]x + 2\cdot y = 0[/tex] and [tex]6\cdot x + 7\cdot y = -10[/tex], then the system of equations in matrix form is:
[tex]\vec A = \left[\begin{array}{ccc}1&2\\6&7\end{array}\right][/tex], [tex]\vec x = \left[\begin{array}{ccc}x\\y\end{array}\right][/tex], [tex]\vec b = \left[\begin{array}{ccc}0\\-10\end{array}\right][/tex]
Then,
[tex]\left[\begin{array}{ccc}1&2\\6&7\end{array}\right]\cdot \left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}0\\-10\end{array}\right][/tex]
Find equations of two lines that cross at the point (2,7) & explain how you got the answer
Given right triangle ABC with altitude BD drawn to hypotenuse AC. If AD =4, BD =6, what is the length of DC
Answer:
[tex]AC=5[/tex]
Step-by-step explanation:
From the question we are told that:
Dimensions
[tex]AD=4\\BD=6[/tex]
Generally the equation for these similar right triangle is mathematically given by
[tex]\frac{AC}{AB}=\frac{AB}{AD}=\frac{BC}{BD}[/tex]
[tex]\frac{AC}{AB}=\frac{AB}{AD}[/tex]
Where
[tex]AD=x[/tex]
[tex]AC=x+4[/tex]
Therefore
[tex]AB^2=x(x+4)[/tex]
Generally the Pythagoras equation for [tex]\triangle[/tex]ADB is mathematically given by
[tex]AB^2=BD^2+AD^2[/tex]
[tex]x(x+4)=4+x^2[/tex]
[tex]x(x+4)-(4+x^2)=0[/tex]
[tex]x^2+4x)-(4+x^2)=0[/tex]
[tex]4x-4=0[/tex]
[tex]x=1[/tex]
Therefore
[tex]AC=x+4[/tex]
[tex]AC=1+4[/tex]
[tex]AC=5[/tex]
Mary has $15.63 left in her wallet after spending $8.01 on snacks. How much did she have in her wallet before she bought the snacks? (Do not put the $ sign in your answer. Just type the amount without the $ sign.
Can someone help me please
Answer:
It's 28
Step-by-step explanation
Which quadratic function in vertex form can be represented by the graph that has a vertex at (3, -7) and passes through the point (1, -10)?
complete the tables of values
Answer:
a=0
b=-8
c=-16
d=0
e=-3
f=-6
Step-by-step explanation:
A rope 24m long is divided into three pieces in a ratio 1:2:5. The length of the shortest piece in
metre is
Answer:
3 m
Step-by-step explanation:
sum the parts of the ratio, 1 + 2 + 5 = 8 parts
Divide the length by 8 to find the value of one part of the rope
24 m ÷ 8 = 3 m ← value of 1 part of the ratio
Thus the shortest piece is 3 m
The required length of the shortest piece is 3 meters.
Given that,
A rope 24m long is divided into three pieces in a ratio of 1:2:5. The length of the shortest piece in meters is to be determined.
The ratio can be defined as the comparison of the fraction of one quantity towards others. e.g.- water in milk.
Here,
let the required proportion is equal to x,
then,
x + 2x + 5x = 24
8x = 24
x = 3
Now the lengths
x = 3 meter
2x = 6 meter
5x = 15 meter
Thus, the required length of the shortest piece is 3 meters.
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Meeta buys a ticket for the movie and a popcorn, which costs $6. She spends $16.50 in all. How much was the movie ticket?
Answer:
10.50
Step-by-step explanation:
16.50-6
Please answer the problem above
Answer:
area of rectangle : 180 sq ft
area of triangle : 30 sq ft
area of entire composite figure : 210 sq. ft
Step-by-step explanation:
rectangle : 15*12= 180
triangle : 15*4=60 /2 = 30
entire : 180 + 30 = 210
Madjeen jogs around the pond by her house twice a day. In the morning, she jogs $3.5$ laps around the pond. In the evening, she jogs $1$ lap around the pond. Madjeen jogs a total of $5.4$ miles. Write and solve an equation to find out how many miles are in each lap around the pond.
Answer:
1.2 miles
Step-by-step explanation:
Morning laps = 3.5 laps
Evening laps = 1 lap
Total miles jogged = 5.4 miles
Total laps made = (3. 5 + 1) = 4.5 miles
Number of miles per laps covered :
Total miles jogged / number f lapses hugged around pond.
= 5.4 miles / 4.5
= 1.2 miles
Therefore, number of miles per round around the pond is 1.2 miles
In QRS the measure of S=90, the measure of Q=29 and SQ=5 feet. find the length of QR to the nearest tenth.r
Answer:
QR ≈ 5.7 ft
Step-by-step explanation:
Using the cosine ratio in the right triangle
cos29° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{QS}{QR}[/tex] = [tex]\frac{5}{QR}[/tex] ( multiply both sides by QR
QR × cos29° = 5 ( divide both sides by cos29° )
QR = [tex]\frac{5}{cos29}[/tex] ≈ 5.7 ( to the nearest tenth )
A cube is made up of squares with sides 3 cm long. What is the surface area of the cube?
9514 1404 393
Answer:
54 cm²
Step-by-step explanation:
Each of the 6 faces of the cube has an area that is ...
A = s² = (3 cm)² = 9 cm²
Then the area of the cube is ...
6 × 9 cm² = 54 cm²
Answer:
Answer:
54 cm²
Step-by-step explanation:
Each of the 6 faces of the cube has has an area that is ...
A= s²=(3cm)²=9cm²Then the area of the cube is ...
6×9cm²= 54cm²Factor the expression: -30x - 15
Answer:
Factored expression: -15 (2x + 1)
What is the percent of change from 800,000 to 600,000?
pls help....which of them is it and no link or I will report
Which of the statements about the y-axis are true? I.The y-axis is a vertical number line that passes through the origin.II.The y-axis intersects the x-axis at the point (0 , 0).III.The y-axis is the first coordinate in an ordered pair that describes the vertical distance from the origin.IV.The y-axis is a horizontal number line that passes through the origin.
Answer:
No i does not well it will be 0,5 or any other number but the x wont change
Step-by-step explanation: