The sum of ages Kate and Gift is 38 years now.What was the sum of their ages five years ago​

Answer:

ABF = 70

Step-by-step explanation:

Since angle EFD is 35, that means that angle AFB is also 35

Single BCD is 75, that means that angle BAF is also 75

Angles in a triangle add up to 180, thus:

75 + 35 + x = 180

x = 70

Answer:

the top one as highlighted

Step-by-step explanation:

y=Mx+c is the equation for a straight line

C is the intercept as it is at 0 it can be dropped from the expression as adding or taking away 0 makes no difference to the end value.

m is the slope

Using translation concepts, the vertices of the rectangle after the translation about the origin by 180° will be as follows:

E'(-4,3), F'(7,-5) and G(-2,-8).

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

The rule for a rotation of 180º about the origin is:

(x,y) -> (-x,-y).

Hence, for triangle EFG, the vertices after the translation will be given as follows:

E'(-4,3), F'(7,-5) and G(-2,-8).

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Answer:

Step-by-step explanation:

A line plot can be used as a data display for the distribution of test scores in math class. Thus, the option to choose is TRUE.

A line plot is a graph that shows data as checkmarks or dots across a number line, indicating the frequency of each value.

The test score in the math test will be discrete data with repeating frequencies. The score of every individual will moreover be a whole number.

The line plot, as we know, marks the dots across the number line, indicating frequency.

Thus, the scores in the math test can be displayed using a line plot, by indicating each type of mark on the line, and dots above those marks for the number of times the same marks occur.

Thus, the option to choose is true.

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Answer:

1.) & 2.) BC and AD are congruent and parallel because in parallelogram opposite sides are equal and parallel

4.) <BCE≅<DAF because they are alternating interior angles bisected by line CA

5.) & 6.) The line BE/DF which bisects the <B/<D iS perpendicular to diagonal CA which forms the right angle

7.) Because sum of any two adjacent angles are 180
8.) This follows ASA Postulate which means that if 2 pair of angles is congruent given that they share a same side, the triangle formed will also be congruent.

Step-by-step explanation:

Take the side CA as the same side of both triangles. This side also participates on the aforementioned angles on the given. The angles <BCE≅<DAF shares the side CA which makes the angles <DFA and <BEC congruent to each other. Therefore, the two right triangles are congruent

Answer: A

Step-by-step explanation:

The y-intercept of f(x) is 3, so clearly we want a shift 5 units down.

Answer:

[tex]\sqrt{16} = 4\\[/tex]

Step-by-step explanation:

the distance formula for graph = [tex]\sqrt{x^{2} + y^{2} }[/tex]

(simplified version)

[tex]\sqrt{0^{2} + (-4)^{2} } \\\\\\\sqrt{0 + 16} \\\\\\\sqrt{16}\\\\= 4[/tex]

I hope its right TT I just looked it up here:

https://byjus.com/maths/distance-between-two-points-formula/

you should double check here as well

The two pairs of polar coordinates for the given point (3, -3) with 0° ≤ θ < 360° are (3√2, 135°) and (3√2, 315°).

A polar coordinate is a two-dimensional coordinate system, wherein each point on a plane is typically determined by a distance (r) from the pole (origin) and an angle (θ) from a reference direction (polar axis).

Next, we would determine the distance (r) and angle (θ) as follows:

r = √(3² + (-3)²)

r = √(9 + 9)

r = 3√2.

θ = tan⁻¹(-3/3)

θ = tan⁻¹(-1)

θ = 3π and 7π/4 (second and fourth quadrants).

Converting to degrees, we have:

θ = 135° and 315°.

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Complete Question:

Determine two pairs of polar coordinates for the point (3, -3) with 0° ≤ θ < 360°

Answer:

b, c, and e

Step-by-step explanation:

a. 3^9 = 3 × 3 × 3× 3 × 3 × 3 × 3 × 3 × 3

= 27 × 27 × 27 => 19683

b. 3^4 = 3 × 3 × 3 × 3

= 9 × 9 => 81

c. -9² =>  81

d. 9^9 = 9 × 9 ×  9 × 9 × 9 × 9 × 9 × 9 ×  9

= 729 × 729 × 729 =>  387420489

e. 81¹ => 81

b, c, and e are all equal to 81

⊱________________________________________________________⊰

Answer:

Step-by-step explanation:

[tex]\LARGE\begin{gathered}\sf{Evaluate \ All \ Expressions \ First} \\ \sf{ 3^9=19683} \\ \sf{ 3^4=81} \\ \sf{-9^2=81, \ or \ -81, \because} \\ \sf{there's \ a \ difference \ between (-9)^2 \ and \ -(9)^2} \\ \sf{(-9)^2=81 \ and -(9)^2=-81} \\ \sf{ 9^9=387,420,489} \\ \sf{0.81^1=0.81\end{gathered}[/tex]

Now, can you see the expressions that are equivalent?

⊰______________________________________________________⊱

Answer:

-1468955

Step-by-step explanation:

please don't forget to write down the correct questions and formula.

find f(x) of g(x)

f(x)=2x+1 and g(x)=x²-7

F of G = 2(x²-7)+1

= 2x²-14+1

= 2x²-13

according to the question x=-1212

so there for f(x) of g(x)=2(-1212)²-13

=-1468955

Answer:

Hope it helps you..............

that is my I hope it helps you

Answer: Circumcenter

Step-by-step explanation: The circumcenter is the point where all perpendicular bisectors of a triangle meet. The 3 perpendicular bisectors of the 3 sides of the triangle meet at the point which is labeled in this triangle as H.

Answer:

AB - Diameter

DA - Tangent

BC - Chord

OA - Radius

CAB - Inscribed Angle

The standard form expression that represents the amount of border material Jessica will need is 8c² + 24c - 6.

Fron the information given, Jessica is using polynomials to represent the dimensions.

The width is 4c² + 5x and the length is 7c - 3. The height is also represented as 2c + 6d.

Here, the standard form expression that represents the amount of border material Jessica will need is 8c² + 24c - 6.

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The transformation can be defined as the introduction of a new set of mathematical coordinates. The correct option is B.

The transformation can be defined as the introduction of a new set of mathematical coordinates that are declared to be different functions of the original coordinates.

As per the given description if the two rigid transformations are used to map ΔABC to ΔXYZ, and the first is a translation of vertex A to vertex X, then the second transformation will be A reflection across the line containing AC.

Hence, the correct option is B.

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Answer:

A   see  picture

Step-by-step explanation:

[tex]\huge\boxed{8\ \text{bags of oranges}}[/tex]

Let's first find how many ounces the basket can hold.

1 pound is equal to 16 ounces. Multiply that to find how many ounces the basket can hold.

[tex]6\cdot16=96[/tex]

Now, divide the weight held by the basket by the weight of each bag of oranges.

[tex]96\div12=\boxed{8}[/tex]

The x-intercepts of the given quadratic function are -2 and 9.

What is a quadratic function?

A quadratic function is a function represented as, f(x) = ax2 + bx + c, with a, b, and c being integers and a not equal to zero. A parabolic curve represents the graph of a quadratic function.

A polynomial's highest degree reveals how many roots the polynomial has. The values for which the polynomial's numerical value is equal to zero are known as a polynomial's roots (also known as zeros of a polynomial). On a graph, the points where the polynomial's graph and the x-axis cross are the roots (x-intercepts).

Roots of the Quadratic Equation

Due to its degree of 2, a quadratic function can only have a maximum of two real roots. In order to find the roots of a quadratic equation, we equate its factors to 0. Thus, in this case, we have,

(x+2)*(x-9)=0

∴ x+2=0

⇒ x=-2

Similarly,

x-9=0

⇒ x=9

Hence, the x- intercepts of the given quadratic function come out to be -2 and 9.

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This is my answer i dont know you like it or not

Answer:

38%

Step-by-step explanation:

2.3/5.98 x 100

= 0.38 x 100

= 38%

The area of the similar triangle named ∆DEF is; 4 square centimeters.

We are given that ∆ABC is similar to ∆DEF.

The perimeter of ∆ABC is five times the perimeter of ∆DEF.  Thus;

(Perimeter of ΔABC) = 5(Perimeter of ΔDEF)

Thus;

(Perimeter of ΔABC)/(Perimeter of ΔDEF) = 5

Thus, we can say that;

Scale factor, K = 5.

Since the area of ∆ABC is 100 square centimeters, Then;

(area of ∆ABC)/(area of ∆DEF) = K²

100/(area of ∆DEF) = 5² = 25.

(area of ∆DEF) = 100/25 = 4.

Thus, the area of ∆DEF is 4 square centimeters.

Complete Question is;

∆ABC is similar to ∆DEF. The perimeter of ∆ABC is five times the perimeter of ∆DEF. The area of ∆ABC is 100 square centimeters. The area of ∆DEF is square centimeters

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The different ways that the students can elect a president and a vice president will be 13110.

The chances of an event occurring are defined by probability. Probability has several uses in games, in business to create probability-based forecasts,

Given data;

Total no of students =  115

The total number of ways to elect a president = 115

If one person is elected as the president the total number of ways to elect a president  = 114

The different ways that the students can elect a president and a vice president are found as;

⇒ 115 ways × 114 ways

⇒ 13110 ways

Hence the different ways that the students can elect a president and a vice president will be 13110.

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Based on the geometric figures shown, the three collinear points are:

Collinear points can be defined as three or more points that all lie on the same straight line (single line). Based on the geometric figures shown in the image below, the three collinear points include:

Another name for line AB is line segment BA, AT, BT, TA, TB. Also, a line in plane Z is line segment AT or line l.

Based on the image shown, the intersection of planes Z and W is line segment AT.

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Answer:

a) 25% are bad

b) 75% are good

Step-by-step explanation:

We know that there are 300 oranges total and that 75 are bad. That means that the rest are good (implied).

300 - 75 = 225 good oranges.

So to find the percentage we have to take the selected amount divided by the total amount.

Bad Apples:                               Good Apples:

75 / 300 = 0.25                          225/300 = 0.75

However, that's a decimal or a number out of 1, we need a percent or a number out of 100. So we have to multiply both numbers by 100.

Bad Apples = 25%

Good Apples = 75%

Answer:

C is the right answer I think

The rational expression that satisfies x = y +-2 is 2xy/(x + y)(x² - 4).

It should be noted that non permissible value is the value of the variable which make the denominator of the rational expression equal to zero.

Based on the information, x + y gives x - y = 0.

x = 2 gives x - 2 = 0

x = -2 gives x + 2 = 0

Ths denominator according to the condition illustrated will be (x - y)(x - 2)(x + 2) = (x - y)(x² - 4)

Then, the rational expression can be written by taking the numerator and denominator. An example will be 2xy/(x + y)(x² - 4).

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Hello,

8(6x-7) <5(9x - 4)

48x - 56 < 45x - 20

48x - 45x < -20 + 56

3x < 36

x < 36/3

x < 12