The quadratic equations are 2b(b - 7) + b = 0 and (4a + 2)(2a - 1) + 1 = 0 .
what is Quadratic Equation?An algebraic equation of the second degree in x is a quadratic equation. The quadratic equation is written as ax² + bx + c = 0, where x is the variable, a and b are the coefficients, and c is the constant term. First, there must be a term other than zero in the coefficient of x² (a ≠ 0) for an equation to be a quadratic equation. The x² term is written first when constructing a quadratic equation in standard form, then the x term, and finally the constant term.
Given:
a) 2b(b - 7) + b = 0
2b² - 14b + b = 0
2b² - 13b = 0
b) (4a + 2)(2a - 1) + 1 = 0
8a² - 4a + 4a + 1 =0
8a² 1 =0
c) 2y + 2(3y - 5) = 0
2y+ 6y- 10 = 0
8y -10=0
d) 8 - 5x = 4(3x - 1)
8- 5x= 12x- 4
Hence, the quadratic equations are 2b(b - 7) + b = 0 and (4a + 2)(2a - 1) + 1 = 0 .
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i need better help understanding slope like how do i find the point on the graph
Solution
The slope of a straight line can be found from any graph by first drawing a triangle against the straight line indicating the rise and the run
The triangle usually is gotten by drawing straight lines from points on the graph where the line passes exactly across the intersection of lines of the y-axis and the x-axis
The circled points are good for usage to get the slope because the line passes exactly at the intersection of the vertical and horizontal line of the graph
Below is how the triangle will look
'The equation for the slope then is written as
[tex]\text{slope = }\frac{y_2-y_1}{x_2-x_1}=\frac{rise}{run}[/tex][tex]\begin{gathered} \text{From the graph as indicated} \\ y_2=8 \\ y_1=2 \\ x_2=\text{ 4} \\ x_1=2 \end{gathered}[/tex]Therefore the slope after substitution is
[tex]\begin{gathered} \text{slope = }\frac{8-2}{4-2} \\ \text{slope}=\frac{6}{2} \\ \text{slope = 3} \end{gathered}[/tex]The slope = 3
a rectangles width is 11 feet more than its length if the perimeter is 54 feet what is the length and width?
Let the length of the rectangle be l and the width be w
width is 11 feet more than length: we can write:
w = 11 + l
Also , perimeter is 54, we can write:
2l + 2w = 54
Note: Perimeter is sum of all sides
Now,
we replace 1st equation in 2nd and find l:
[tex]\begin{gathered} 2l+2w=54 \\ 2l+2(11+l)=54 \\ 2l+22+2l=54 \\ 4l=54-22 \\ 4l=32 \\ l=\frac{32}{4} \\ l=8 \end{gathered}[/tex]w is 11 + l
So,
width is 11 + 8 = 19
Length = 8 feet
Width = 19 feet
/ Week 1 / Week 1 Monday - Daily Quiz
A rectangle is 5 feet long and 12 feet wide.
What is it's area?
60 feet² is the area of rectangle.
What is rectangle?
A rectangle is a sort of quadrilateral with parallel sides that are equal to one another and four vertices that are all 90 degrees apart. As a result, it is sometimes referred to as an equiangular quadrilateral. Rectangles can also be referred to as parallelograms because their opposite sides are equal and parallel.The four sides of a laptop are equal in length and have opposite sides that are parallel to one another.length = 5 feet
wide = 12 feet
area of rectangle = length × width
= 5 × 12
= 60 feet²
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Find the volume of this figure
Answer: 704 ft^3
Step-by-step explanation:
8 ft x 8 ft x 8 ft = 512 ft^3
(8 ft x 8ft x 9 ft)/3 = 192 ft^3
512 ft^3 + 192 ft^3 = 704 ft^3
Choose the expression that is equivalent to the one shown
1. Rewrite the expression to get the numerator and denominator with the same base:
[tex]\frac{(2^3)^{12}}{(2^2)^3}=\frac{2^{36}}{2^6}[/tex]2. Divide by leavinfg the same base and subtracting the exponents:
[tex]\frac{2^{36}}{2^6}=2^{36-6}=2^{30}[/tex]Write the result with base 4:
[tex]2^{30}=(2^2)^{30/2}=4^{15}[/tex]As you can see above any of the given expression is equivalent to the given expression.Answer: none of thesehow many 725ml is in liters?
ANSWER
There are 0.725L in 725mL
EXPLANATION
Given that
The volume in mL is 725mL
Follow the steps below
Recall, that 1mL is equivalent to 0.001L
Let x represents the volume in Liters
[tex]\begin{gathered} \text{ 1mL }\rightarrow\text{ 0.001L} \\ \text{ 725mL }\rightarrow\text{ xL} \\ \text{ cross multiply} \\ \text{ 1mL }\times\text{ xL = 725mL }\times\text{ 0.001L} \\ \text{ isolate xL} \\ \text{ xL = }\frac{725\cancel{mL}\times\text{ 0.001L}}{1\cancel{mL}} \\ \text{ xL = 725 }\times\text{ 0.001} \\ \text{ x = 0.725L} \end{gathered}[/tex]Therefore, there are 0.725L in 725mL
The side view of a tire resembles a doughnut. If the inner diameter is 11.0 in. and the out diameter is 25.0 in., what is the area (in square inches) of the side of the tire?
If the side view of a tire resembles a doughnut. If the inner diameter is 11.0 in. and the out diameter is 25.0 in., Then area of the side of tire is 92237.5 inches.
What is Circle?A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.
A doughnut is a surface of revolution generated by revolving a circle in three-dimensional space about an axis that is coplanar with the circle.
A doughnut has two circles. One circle with in the other circle.
The diameter of inner circle is 11.
So radius of inner circle is 5.5 inches.
The diameter of outer circle is 25 inches.
The outer circle add diameter of inside circle.
25+11=36 inches.
The radius of outer circle is 18 iches.
The area of doubtnut
Area of big circle - Area of small circle or inner circle
Area of doubtnut= πR²-πr²
R outer radius= 18
r inner radius =5.5
Area of doubtnut= 3.142 (R²-r²)
=3.142(18²-5.5²)
=3.14(324-30.25)
=3.14(293.72)
=92237.5 inches
Hence the area of the side of the tire is 92237.5 inches
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Describe all of the transformations applied to the parent function f(x) = x² to sketch g(x) = 4(x – 2)² – 5
The transformations required are to shift the graph to the right by 2 units, shrink the graph by a factor of 4 and shift the graph downwards by 5 units.
The parent function given to us is f(x).The function f(x) equals x².We need to sketch the function g(x).The function g(x) equals 4(x – 2)² – 5.First of all, we need to graph x².Then, for the graph of (x – 2)², we need to shift the previous graph to the right by 2 units.Then, to obtain the graph for 4(x – 2)², we will shrink the graph by a factor of 4.Finally, to get the graph for 4(x – 2)² – 5, we will shift the graph in a downward direction by 5 units.Hence, we will obtain our final graph.To learn more about functions, visit :
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A candy stand sells lollipops, gumballs, and chocolates. The gumballs cost 5 cents more than the chocolates. The lollipops cost twice as much as the chocolates. A particular handful containing 3 gumballs, 2 lollipops, and 7 chocolates costs $2.11. What is the cost of each item?
The cost of lollipops, gumballs, chocolate is $ 0.268, $0.184, $0.134
What is an equation?
An equation is a formula that describes the equality between two expressions, by connecting them with the equals sign '='.
Let the cost of lollipops be x
The cost of gumballs be y
and cost of chocolates be z
We are given that the gumballs cost 5 cents more than the chocolates
mathematically this can be written as
[tex]y=z+0.05[/tex]
Similarly,
The lollipops cost twice as much as the chocolates
mathematically this can be written as,
[tex]x=2z[/tex]
Now finally we purchase 3 gumballs, 2 lollipops and 7 chocolates
The equation can be given as,
[tex]3x+2y+7z=2.11[/tex]
Substituting the values of x and y in this equation we get,
[tex]6z+2(z+0.05)+7z=2.11\\6z+2z+0.1+7z=2.11\\15z=2.01\\z=0.134[/tex]
The cost of chocolates is $0.134
The cost of gumballs is $0.184
And the cost of lollipops is $0.268
Hence, The cost of lollipops, gumballs, chocolate is $ 0.268, $0.184, $0.134
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-10+*+5> 7-5
3
3. Here is an inequality:
What value of x will make the two sides equal?
35 225
4
Fraction, A number that is stated mathematically as a quotient, where the numerator and denominator are divided. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.
What is denominator?A fraction is a portion of a whole or, more broadly, any number of equal parts. In everyday English, a fraction describes the number of parts of a specific size, such as one-half, eight-fifths, or three-quarters. The denominator is simply the bottom number.
-10+*+5>7-5 justification
-10+*+5> 7-5
Step 1:
Multiply
-10 * 5 = -50.
Step 2:
Subtract:
7 - 5 = 2
the result of step No. 1 > the result of step No. 2
= -50 > 2 = No
The result:
-10 * 5> 7 - 5 = No
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A rectangular carport has area 150 square feet. The height of the carport is five feet less than twice its length. Find the height and the length of the carport.
We are given that the area of a rectangle is 150 square feet. If "h" is the height and "l" is the length then the area is given by:
[tex]hl=150[/tex]We are also given that the height is 5 feet less than twice its length, this can be written mathematically as:
[tex]h=2l-5[/tex]Now we can replace the value of "h" in the equation for the area:
[tex](2l-5)l=150[/tex]Now we use the distributive property:
[tex]2l^2-5l=150[/tex]Now we have a quadratic equation that can be written as:
[tex]2l^2-5l-150=0[/tex]We can factor this equation to determine the values of "l". We multiply and divide by 2:
[tex]\frac{4l^2-5(2l)-300}{2}=0[/tex]Factoring in the numerator:
[tex]\frac{(2l-20)(2l+15)}{2}=0[/tex]Now we take common factor in the first parenthesis in the numerator:
[tex]\frac{2(l-10)(2l+15)}{2}=0[/tex]Simplifying:
[tex](l-10)(2l+15)=0[/tex]Now we set each factor to zero:
[tex]\begin{gathered} l_1-10=0 \\ l_1=10 \\ 2l_2+15=0 \\ l_2=-\frac{15}{2} \end{gathered}[/tex]We take the positive value, therefore, the length of the rectangle is 10 feet. Now we replace this value in the equation for the height.
[tex]h=2(10)-5[/tex]Solving we get:
[tex]\begin{gathered} h=20-5 \\ h=15 \end{gathered}[/tex]Therefore, the height of the rectangle is 15 feet.
Robert has attended 32 out of 40 soccer practices this year. Based on his record of attendance, which is
the probability that Robert will attend soccer practice in the future?
Step-by-step explanation:
he attended 32 of 40.
that was a rate
32/40 = 4/5 = 0.8
if he keeps the same ratio, then the probability for him to attend any soccer practice in the future is 0.8.
7/8 ^2
Choose the correct expanded form for the following expression .
Evaluate 7/8^2
The correct expanded form for the following expression is 7/8 × 7/8.
What is expanded form?The division of numbers into their component ones, tens, hundreds, thousands, ten thousand, and so forth creates the expanded form of the number. The expanded version of the number is the sum of each digit times its place value, which is used to represent the number. A number is broken down to show the value of each of its digits in order to be written in expanded form. 144 would then be converted to 100 + 40 + 4 = 144. It can be used to compute sums as well. When a number is expanded to show the value of each digit, it is written in expanded form. The numerical value of each digit in the number we are writing is represented using extended form.
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In a rectangle the base measures (x + 7), height (x + 2), area = 36 cm
Calculate perimeter, height and base.
The values are given as;
Perimeter = 26cm
Height = 4cm
Base = 9cm
How to determine the valueThe formula for determining the area of a rectangle is expressed as;
Area = lw
Where;
l is the length of the rectanglew is the width of the rectangleNow, substitute the values into the formula, we have;
36 = (x +7)(x + 2)
Now, expand the bracket
36 = x^2 + 2x + 7x + 14
collect like terms
36 = x^2 + 9x + 14
Make into quadratic equation
x^2 + 9x + 14 -36 = 0
x^2 + 9x - 22 = 0
Factorize the equation
x^2 + 11x - 2x - 22 = 0
Factorize further
x(x + 11) - 2( x + 11) = 0
Then, x - 2 = 0, x = 2
or x + 11 = 0
x = -11
Height = x + 2 = 4cm
Base = x + 7 = 9cm
The formula for perimeter is expressed as;
Perimeter = 2( l +w )
Perimeter = 2( 4 + 9)
Perimeter = 2(13)
Perimeter = 26 cm
Hence, the values are 26cm, 4cm and 9cm respectively.
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which measurement is closest to the volume of the container in cubic inches
The volume of a cylinder is given as;
[tex]\begin{gathered} Vol=\pi\times r^2\times h \\ r=3 \\ h=10.5 \\ \text{Vol}=3.14\times3^2\times10.5 \\ Vol=3.14\times9\times10.5 \\ \text{Vol}=296.73in^3 \end{gathered}[/tex]Therefore, from the options provided, the closest to the volume of the container is 296.88 cubic inches.
Option B is the correct answer
CALCULATOR COLOR THEME Q Q 4. Find the area of the shaded region. 4 in. 8 in. 4 in 12 in
We are asked to determine the area of the shaded region. there are two squares, to determine the area we need to find the area of the outer rectangle and subtract the area of the interior rectangle. Let's remember that the area of a rectangle is the product of its sides. Therefore, the area of the outer rectangle is:
[tex]\begin{gathered} A_0=(8in)(12in) \\ A_0=96in^2 \end{gathered}[/tex]Now we find the area of the interior rectangle:
[tex]\begin{gathered} A_i=(4in)(4in) \\ A_i=16in^2 \end{gathered}[/tex]Now we subtract the areas:
[tex]A=A_o-A_i[/tex]Replacing:
[tex]\begin{gathered} A=96in^2-16in^2 \\ A=80in^2 \end{gathered}[/tex]Therfore, the area of the shaded area is
6.5 in. 5 in 7.5 in. What is the total surface area of this prism in square inches?
6.5 in. 5 in 7.5 in. What is the total surface area of this prism in square inches?
we have that
the total surface area of a prism is equal to
SA=2B+Ph
where
B is the area of the base
P is the perimeter of the base
h is the height of the prism
Let
L=6.5 in
W=5 in
H=7.5 in
so
B=L*W=(6.5*5)=32.5 in2
P=2(L+W)=2(6.5+5)=23 in
H=7.5 in
therefore
SA=2(32.5)+23(7.5)
SA=237.5 in2
surface area is 237.5 square inchessee the attached figure to better understand the problem
the surface area is the area of its six rectangular faces
so
SA=2(6.5)8(5)+2((5)(7.5)+2(6.5)*(7.5)=237.5 in2
Which situation is the best modeled by a nonlinear function with time as the independent variable?
The most accurate model for a quadratic regression is a nonlinear function with time as the independent variable.
A non-linear relationship between the independent and dependent variables is stated in the regression model.
Along with the independent variable's square, it also contains the dependent variable.
The equation is Y=ax²+bx+c
When the independent variable is called x, and the dependent variable is called y.
Here, a, b, and c are the constant variable.
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Use the figure to the right to name each of the following.1. A line2. A plane
ANSWER and EXPLANATION
We want to name a line and a plane.
LINE
In naming a line, we use two lettters. The two letters are the letters at the beginning and the end of the line.
Now, from the diagram, we have the following lines:
- nY
- Xm
- Zl
PLANE
A plane is made up of two lines intersecting one another.
In naming a plane, three letters are used, with the letter at the intersection in the middle.
The planes in the diagram are:
- mYn plane
- lRm plane
The Earth has an eccentricity of 0.017. Which of the three ellipses that you calculated do you think is the most similar in eccentricity to the Earth’s orbit? Why?
SOLUTION
Eccentricity means a measure of how much the deviation of the curve has occurred from the circularity of the given shape.
Of the three ellipses, the eccentricity is
[tex]\begin{gathered} \text{Ellipses 1=0.21} \\ \text{Ellipses 2=}0.4 \\ \text{Ellipses 3=0.64} \end{gathered}[/tex]Ellipses 1 has an eccentricity closer to the eccentricity of the Earth
Hence
Ellipses 1 is the most similar in eccentricity to the Earth's orbit
Use the slope-intercept form of the linear equation to write the equation of the line with the given slope and v-intercept Slope - 9. y-intercepto 0.-)
the equation of the line will be
[tex]y+\frac{7}{9}=-9x[/tex]then subtracting 7/9 in both sides we have
[tex]y=-9x-\frac{7}{9}[/tex]which is the line equation in slope intercept form.
use the image to find angles Q & U. explain your reasoning.
Solution
Given
[tex]\begin{gathered} m<3=45^0 \\ m<1=50^0 \\ m<6=135^0 \end{gathered}[/tex][tex]\begin{gathered} m<6\text{ = m<1 + m<2 + m<3 \lparen corresponding angles are equal\rparen} \\ 135=50+m<2+45 \\ 135=95+m<2 \\ m<2=135-95 \\ m<2=40^0 \end{gathered}[/tex][tex]\begin{gathered} mThe slope-intercept equation of a line is y= 4x-1. What is the slope of the line?
OA. The slope is 4.
OB. The slope is -4.
OC. The slope is -1.
OD. The slope is 1.
The figure below is a net for a triangular prism. What is the surface area of the triangular prism, in square feet?
The figure consists of,
A rectangle with dimension 15 ft by 7 ft.
Two triangles with base b = 7 ft and height h = 5 ft.
A rectangle with dimension 15 ft by 5 ft.
A rectangle with dimension 15 ft by 8.6 ft.
Determine the surface area of triangular prism.
[tex]\begin{gathered} A=15\cdot7+2\cdot\frac{1}{2}\cdot7\cdot5+15\cdot5+8.6\cdot15 \\ =105+35+75+129 \\ =344 \end{gathered}[/tex]So, surface area of triangular prism is 344 square feet.
HELP PLEASEEEEEEEEEEEWE
Answer:
Answers are in the image
Step-by-step explanation:
Hope I got everything right and hope that helps you
It was recently estimated that females outnumber males by about three or two. If there are 1770 people in a county, how many of them are females?
GIVEN
1) Females outnumber males by 3 to 2.
2) There are 1770 people in the city.
SOLUTION
Let the number of males be x and the number of females y. Therefore, the total number of people can be written to be:
[tex]x+y=1770\text{ -----------(1)}[/tex]If there are 3 females for every 2 males, we have that:
[tex]\begin{gathered} \frac{y}{3}=\frac{x}{2} \\ \therefore \\ x=\frac{2y}{3}\text{ ----------(2)} \end{gathered}[/tex]We can substitute equation (2) into equation (1) and solve for y:
[tex]\begin{gathered} \frac{2}{3}y+y=1770 \\ \frac{2y+3y}{3}=1770 \\ 5y=1770\times3 \\ 5y=5310 \end{gathered}[/tex]Dividing both sides by 5, we have
[tex]y=1062[/tex]There are 1062 females in the county.
If f(x) = x^4 − x^3 + x^2 and g(x) = −x^2, where x ≠ 0, what is (f ⁄g)(x)?
The correct answer is
[tex](\frac{f}{g})(x)=-x^2+x-1[/tex]To solve this, first let's write the division:
[tex]f(x)=x^4-x^3+x^2,g(x)=-x^2\Rightarrow(\frac{f}{g})(x)=\frac{x^4-x^3+x^2}{-x^2}[/tex]Now we can factor out a x^2 on the top and the bottom of the expression:
[tex](\frac{f}{g})(x)=\frac{x^4-x^3+x^2}{-x^2}\Rightarrow(\frac{f}{g})(x)=\frac{x^2(x^2-x+1)}{x^2(-1)}[/tex]Now we can cancel out and divide by (-1), or the same thing, multiply by (-1):
[tex](\frac{f}{g})(x)=\frac{x^2(x^2-x+1)}{x^2(-1)}=-(x^2-x+1)=-x^2+x-1[/tex]Then the answer is (f/g)(x) = -x^2 + x - 1. That's the third option
3) Triangle ABC is dilated by a scale factor of 4 to form triangle A'B'C'. Wha-are the coordinates of vertex A'? Make sure that you enter the coordinatesin the form of (x, y) below. *Your answer
Answer
A' (-8, 4)
Explanation
When a figure, that is on the coordinates system is dilated (that is, enlarged or reduced) with respect to the origin, the new coordinates of its edges is simply a product of its old coordinates and the scale factor.
For this question, the coordinates of A is (-2, 1) and the dilation of the triangle ABC is by a scale factor of 4.
So, the new coordinates of A will be calculated thus
A (x, y) = A' (x × scale factor, y × scale factor)
A (-2, 1) = A' (-2 × 4, 1 × 4) = A' (-8, 4)
Hope this Helps!!!
solve for x. round to nearest tenth. angle DEF is an equilateral triangle. hyp is 24
Since the triangle DEF is an equilateral triangle and x is the height of this triangle, we can use the following formula for the height of an equilateral triangle:
[tex]h=\frac{l\sqrt[]{3}}{2}[/tex]Where 'l' is the length of the triangle side.
So, using l = 13, we have:
[tex]\begin{gathered} x=\frac{13\cdot\sqrt[]{3}}{2} \\ x=\frac{13\cdot1.73}{2} \\ x=11.2 \end{gathered}[/tex]So the value of x is 11.2
If f(x) = -2x^2 + 6 and g(x) =3xm evaulate the expressions below:
a. f(-1) + g(4)
b. 2g(2) - 7
Answer:
a
Step-by-step explanation:
